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<p>The famous example of a dripping faucet is an example of a Rayleigh-Plateau instability in which there is a certain jet radius below which perturbations on the surface will grow to break the jet into droplets. The drop radius, according to this theory, can be predicted by calculating the fastest growing unstable wav...
g15276
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<p>We usually have the normalization (see e.g. page 110 in Halzen &amp; Martin "Quarks and Leptons")</p> <p>$$u^{(r)\dagger}u^{(s)} = 2E\delta_{rs}$$ which leads to $${\bar{u}^{(s)}}u^{(s)} = 2m. $$</p> <p>According to the authors of the cited book, in the Breit frame in elastic electron proton scattering$^2$, the n...
g15277
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<p>What is the difference between the light rays reflected from a mirror and rays directly emmited from a screen if the screen shows the same image as the mirror would.</p>
g15278
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<p>I'm a bit messed up with conservation laws and continuity equations.</p> <p>This is my understanding: </p> <ul> <li><p>A <a href="http://en.wikipedia.org/wiki/Conservation_law" rel="nofollow">conservation law</a> describes that a physical quantity $G$ is conserved with time. It does not prevent "quantity teleporta...
g15279
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<p>If, in local system, an accelerated system is completely physically equivalent to a system inside a gravitational field.</p> <p>Acceleration results in an increase in speed. Right?</p> <p>What happens when the accelerated "elevator" accelerates to the point where its speed hits (or exceeds?) the speed of light? ...
g473
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<p>Edward Nelson's book "Quantum Fluctuations" (Princeton UP, 1985) gives an alternative way to introduce trajectories, quite different to the trajectories of de Broglie-Bohm type approaches. I've read the book in the past and university libraries generally have copies, but I've been unable to find a good open web refe...
g15280
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<p>I have a very fundamental question. We explain polarisation of light assuming wave nature of light. Is it still valid if we assume light as photons? Or in other words, polarisation is a wave concept or applicable to individual photons as well?</p> <p>May be this is my wrong concept! I feel some confusion here.</p>
g15281
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<blockquote> <p><em>The world's largest ball of a string is about $R=2 m$ in radius. To find the nearest order of magnitude, what is the total length $L$ of the string in the ball?</em></p> </blockquote> <p>I have tried this in the following way</p> <p>Total volume occupied by string $v=(cross\ section\ area\ d^2)\...
g15282
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<p>I need to spec a motor to turn a mixing barrel. The barrel contains loose earth and can be filled to a maximum of 50% of its interior volume. It is a horizontal cylinder, and will rotate through its central axis. What effort/torque is required to start the barrel turning?</p> <p>In my case, the mass of the barrel w...
g15283
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<p>I just got myself an <a href="http://en.wikipedia.org/wiki/Infrared_thermometer">infrared thermometer</a>. I wouldn't have been able to predict what temperature it would give me when pointing at the sky, but it turned out to be -2 °C the first time I measured, and slightly going up and down with the temperature on t...
g15284
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<p>In order to compute the fine structure of the terms in LS coupling (Russell-Saunders coupling), we must treat the hamiltonian $$H_2 = \sum_{\mbox{open subshells}} \xi(r_i) \vec{l_i}\cdot\vec{s_i}$$</p> <p>as a perturbation to the perturbation given by the hamiltonian $$H_1 = \sum_{\mbox{open subshells}}\frac{1}{r_...
g15285
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<p>This is probably a pretty elemental question, but I can't figure out what the concept is called or how to calculate it. Say you have a solid cone shaped piece of ice, you hold it in your hand and squeeze the cone and it slips up as you continue the same force until it slips all the way up and out of your grip. What ...
g15286
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<p>A SQUID works using the concept that flux going through a superconducting circuit is quantized. So, if we try to change the magnetic field smoothly, the circuit will produce a screening current that would create a flux that cancels the difference between the applied flux and the previous/next quantum of the flux dep...
g15287
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<p>Recently many LHC-affiliated organizations and otherwise announced the Higgs ML learning challenge (in May) running over the summer. There are many competing teams and significant results posted already.</p> <p>Is this contest duplicating analysis that has been done inside LHC teams already, looking for better Higg...
g15288
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<p>I have been struggling with these Majorana fermion identities for quite sometime now. I would be grateful if someone can help me with them. </p> <p>Let $\lambda$,$\theta$ and $\psi$ be $4$-component Majorana fermions. Then apparently the following are true,</p> <ul> <li><p>$(\bar{\theta}\gamma_5 \theta)(\bar{\psi}...
g15289
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<p>Water molecules and various salt molecules are very different. However, it seems very difficult to separate the two. Once a salt is dissolved in water, an energy or chemical intensive method (like boiling) is required to separate the salt back out again. Why is this? </p>
g15290
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<p>I am reading "<em>An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements by J. R.Taylor</em>", and I read the following formula in an exercise:</p> <p>$$\chi^2_\text{adjusted}=\sum_{k=1}^2\frac{\left (|O_k-E_k|- \frac{1}{2}\right )^2}{E_k}$$</p> <p>but I don't know when using it! In...
g15291
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<p>In Nielsen and Chuang's text on Quantum Information and Computation, the measurement postulate is stated by using a collection of measurement operators and the outcomes are the indices of the measurement operators. See: <a href="http://books.google.com/books?id=65FqEKQOfP8C&amp;lpg=PA87&amp;ots=Pq9S_kl6GO&amp;dq=mea...
g15292
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<p>The standard textbook treatment of the conformal gauge for a free string with BRST ghosts is fine, but when a string splits into two, we have Gribov ambiguities for the conformal gauge. We can impose the conformal gauge for the initial string before the split, and also the final two strings after the split, but not ...
g15293
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<p>In 2000, Nasa conducted an experiment and found that gravity plays an indirect role in flame formation and composition (see the <a href="http://en.wikipedia.org/wiki/Flame" rel="nofollow">wikipedia article</a>). What role does gravity play? Why does a flame extend in the opposite direction of gravity? Assuming th...
g15294
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<p>I have always seen a bicycle not standing without any support, it either falls down to the right or to the left, may even to some other direction. But,the same two wheeler when under motion,moves balanced, without falling to either side,even it not falls, when the two wheeler is bent to left or right by the driver, ...
g408
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<p>Just as background, I should say I am a mathematics grad student who is trying to learn some physics. I've been reading "The Theoretical Minimum" by Susskind and Hrabovsky and on page 134, they introduce <em><a href="http://en.wikipedia.org/wiki/Infinitesimal">infinitesimal</a> transformations.</em> Here's the first...
g15295
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<p>I just started to read Srednicki's <a href="http://web.physics.ucsb.edu/~mark/qft.html" rel="nofollow"><em>QFT</em></a> and I have a problem here. I thought the order of creation operator and projected hamiltonian should be in reversed order ( here I mean H ~ wba, where a is annihilation and b is creation operator, ...
g15296
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<p>What is the expression for the WKB transmission probability in momentum space?</p>
g15297
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<p>Something I've taken for granted and not yet thought about physically, is how the frequency of quasinormal modes related to a black hole are $\textit{complex}$.</p> <p>I know that it's something to do with the fact that these modes decay but I tried to explain it to myself with several different reasonings, none of...
g15298
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<p>Consider the following metric</p> <p>$$ds^2=V(dx+4m(1-\cos\theta)d\phi)^2+\frac{1}{V}(dr+r^2d\theta^2+r^2\sin^2\theta{}d\phi^2),$$</p> <p>where $$V=1+\frac{4m}{r}.$$</p> <p>That is the <a href="http://www.google.com/search?as_epq=Taub+NUT+instanton" rel="nofollow">Taub-NUT instanton</a>. I have been told that it ...
g15299
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<p>In a vapor-compression refrigeration system I would like to understand the following :</p> <ol> <li><p>Why is there a need for the compressor ? Can't the saturated vapor from the evaporator be cooled directly in the condenser ? Why does it need to be a superheated vapor in order to be condensed ?</p></li> <li><p>Ho...
g15300
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<p>I am now playing with a permanent magnet made of Neodymium.</p> <p>It is impressively strong.</p> <p>A question is, is the magnetization direction of the magnet fixed relative to its crystal structure?</p>
g15301
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<p>I'm reading Lanczos's <em>The variational principles of mechanics</em>, and on pp. 80-81 there is an example involving a system made up of $n$ rigid bars, freely jointed at their end points, and the two free ends of the chain being suspended.</p> <p>The coordinates are chosen so that the $x$ axis is horizontal, and...
g15302
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<p>I have a question that came up in a discussion with friends. If I throw a ball straight up in an enclosed train car moving with constant velocity, I believe the basic physics books say it will land in the same spot. But will it really? I think I can say that the answer is "not in the real world".</p> <p>Triviall...
g15303
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<p>The normal force obviously always has direction perpendicular to the surface of contact, but I'm a bit confused about its sense: is it going 'up' or 'down'? I've seen articles on the web that describe the normal force as going either way.</p> <p>My own reasoning would tell me that since force of friction is depende...
g15304
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<blockquote> <p><strong>Possible Duplicates:</strong><br> <a href="http://physics.stackexchange.com/questions/14973/what-would-be-the-immediate-effects-if-light-does-not-go-at-the-maximum-speed-pos">What would be the immediate effects if light does not go at the maximum speed possible?</a><br> <a href="http://phy...
g83
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<p>Tangential components of the electric field across an interface between two media, with no impressed magnetic current densities along the boundary of the interface, are continuous. So: $ n \times (E_2 - E_1) = 0$. Now suppose an lumped<img src="http://i.stack.imgur.com/SE9fd.png" alt="enter image description here"> ...
g15305
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<p>As far I know they come from accelerator collisions, but I have read confusing things like <em>magnetically focused</em>. How could neutrinos be guided magnetically if they aren't affected by the electromagnetic field?</p> <p>I would like to have a better idea of how neutrinos are emitted.</p>
g15306
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<p>How do I find the supporting force $R_A$ and the moment $M_A$?</p> <p>Should I use the sum of moments or?</p>
g15307
[ 0.025429697707295418, 0.0027094611432403326, -0.029275862500071526, -0.06441696733236313, 0.04740249738097191, -0.048228245228528976, -0.006441871635615826, 0.016620179638266563, 0.0017891393508762121, 0.0044579897075891495, -0.024417225271463394, -0.04986552149057388, -0.029467688873410225,...
<p>This may seem like a slightly trite question, but it is one that has long intrigued me.</p> <p>Since I formally learned classical (Newtonian) mechanics, it has often struck me that angular momentum (and generally rotational dynamics) can be fully derived from normal (linear) momentum and dynamics. Simply by conside...
g824
[ 0.05115099996328354, -0.03486208617687225, 0.011019148863852024, -0.05664490908384323, 0.052733100950717926, -0.0007006110390648246, 0.02619047462940216, -0.00886314082890749, 0.017104992642998695, 0.026973506435751915, 0.05024350434541702, -0.03904343396425247, -0.017891408875584602, -0.0...
<p>If the force (at 90∘ to the lever arm) applied is 15 N and it is applied at 2.0 m from the pivot point (point of rotation), what is the torque on the lever?</p> <p>Is it 30.0 N/m? </p>
g15308
[ 0.026711178943514824, -0.018500057980418205, 0.012622474692761898, -0.052815768867731094, 0.047681666910648346, 0.03160954639315605, 0.06444881111383438, -0.023614343255758286, -0.03963995352387428, 0.004031769465655088, -0.03212467208504677, -0.016418036073446274, -0.02684565633535385, -0...
<p>I am confused about what it is exactly that a reduced density operator describes. To illustrate, I came across the following seemingly paradoxical argument.</p> <p>Consider a biparte system $AB$, described by the pure state:</p> <p>$$| \psi \rangle = \sum_{a,b} \psi(a,b) |ab \rangle$$</p> <p>Its density matrix is...
g15309
[ 0.037972431629896164, 0.00045741809299215674, -0.01602023094892502, 0.0033051911741495132, 0.04213680326938629, 0.01023795921355486, 0.023878157138824463, 0.00397117342799902, 0.030019909143447876, -0.033252276480197906, -0.017833758145570755, -0.009490657597780228, 0.028370173647999763, -...
<p>In many equations we see infinitesimals $dA$, $dS$, $dx$ and so on. What is is the physical significance of these? Someone told me it signifies a small entity. For example,in case of $dA$ it signifies a small area, in case of $dS$ it signifies a small surface,etc. What does it really mean?</p>
g15310
[ -0.026995282620191574, 0.054956164211034775, -0.028272036463022232, -0.0900585874915123, 0.010136902332305908, 0.028583122417330742, 0.04218771681189537, 0.05171725153923035, -0.014917289838194847, -0.05927921459078789, -0.017185254022479057, -0.005439864471554756, 0.09961870312690735, -0....
<p>The body 'A' is moving forward with certain acceleration over the ground. The ground applies a kinetic friction force on 'A' in backward direction to oppose the relative motion. The block 'A' also applies an equal and opposite force of friction on the ground, would that force of <a href="http://en.wikipedia.org/wiki...
g15311
[ 0.10337673127651215, 0.05886335298418999, 0.006646683439612389, 0.010710407048463821, 0.04134475067257881, 0.02626333013176918, 0.09958187490701675, 0.04445647820830345, -0.03866097331047058, -0.04128500819206238, 0.016834378242492676, -0.02367124706506729, -0.00365993520244956, 0.02345076...
<p>By newton's third law , we know that every action has an equal and opposite reaction .We move left when we push slightly on the right and move forward as we push backward . But how do rockets , satellites etc change their direction in the space as they have nothing to push on? </p>
g15312
[ 0.004504200536757708, 0.027051227167248726, -0.002862643450498581, 0.03257308155298233, 0.04550834000110626, 0.059951987117528915, 0.0012550543760880828, 0.01918455958366394, 0.01719866693019867, -0.0349704772233963, -0.006031296215951443, -0.013486776500940323, 0.025084249675273895, -0.00...
<p>I have a question about electromagnetism. Probably I understand something in a wrong way. So, I know that the <a href="http://en.wikipedia.org/wiki/Drift_velocity" rel="nofollow">drift velocity </a> of electrons in conductors is very small ($\sim$ $0.1$-$1$ mm / s). Also I know that if I put the compass to the wire,...
g15313
[ 0.034594662487506866, -0.0038260645233094692, -0.006930328905582428, 0.02450735494494438, 0.05919606611132622, 0.05183171108365059, 0.054467152804136276, -0.04123306646943092, -0.040792666375637054, 0.033204466104507446, -0.03236570954322815, 0.031215671449899673, -0.013655170798301697, -0...
<p>How can I simulate a rigid sword bounced from a wall and hit the ground(like in physical world)?</p> <p>I want to simulate a simple animation.</p> <p>The sword is controlled by a center/mass point.(Actually finally it't in a game engine).</p> <p>I can detect the figure and the size of the sword(maybe needed in do...
g15314
[ 0.0528143085539341, 0.05098061263561249, -0.021406058222055435, 0.009562651626765728, 0.005739022511988878, 0.00864788331091404, 0.04532812535762787, -0.04143565893173218, -0.054780855774879456, -0.02302093245089054, -0.0016577801434323192, 0.02499529719352722, 0.05824939161539078, -0.0445...
<p>I have a mini quadcopter controlled by remote controller. I have set the motors (e.g 50% thrust) it will remain at altitude at 10 cm~ but once I increase to 80% and then follow by decrease to 50% I should remain at a certain altitude (e.g 2 meters) but it will then drop back down to 10cm~. My question is, why does i...
g15315
[ 0.0562632754445076, -0.013840633444488049, 0.011932351626455784, 0.07465283572673798, 0.026257548481225967, 0.04373512417078018, -0.006335599347949028, -0.018112357705831528, -0.05012129992246628, -0.03804560750722885, 0.003403395414352417, 0.018978876993060112, -0.0079595185816288, 0.0070...
<p>Why String theory ? simple cosmological model is not sufficient for study of nature of universe</p>
g15316
[ -0.0303084384649992, 0.026087841019034386, 0.03761976957321167, -0.02365989051759243, -0.0104057053104043, 0.034812744706869125, -0.007277204189449549, -0.026064850389957428, -0.007066821679472923, -0.06876732409000397, 0.02754412218928337, -0.037754956632852554, 0.044536057859659195, 0.04...
<p>The speed of sound is the rate that disturbances in air propagate through it.</p> <p>Is it possible to have a wind that itself is moving at supersonic speeds relative to stationary winds around it?</p> <p>Or perhaps a fluid flowing through a pipe at a speed greater than the speed of sound within it.</p> <p>If so,...
g15317
[ 0.071137934923172, 0.022893987596035004, 0.01237974502146244, 0.002707758219912648, 0.015045658685266972, -0.006504653487354517, 0.00031508129904977977, 0.03579400107264519, -0.05609837546944618, -0.03812405839562416, 0.02071322500705719, 0.014205708168447018, -0.019811855629086494, 0.0561...
<p>I know from the book that electrons will be kicked out from the metal plate if the light of appropriate wavelength is exposed to the metal plate. </p> <p>My mental model says if we let the light expose the plate in a long enough interval, the plate will have no electrons anymore. So what happens on the plate? Does ...
g15318
[ 0.10164567828178406, 0.03986913338303566, -0.005243237130343914, -0.02348330430686474, 0.035529784858226776, 0.042513567954301834, -0.008475341834127903, 0.02242155186831951, 0.001738899853080511, 0.015749366953969002, -0.034773994237184525, 0.11890976130962372, -0.048405252397060394, 0.01...
<p>Consider the coordinate transformation $$ \tilde x^a=x^a+\frac{1}{2}\Gamma^a_{bc}x^bx^c $$</p> <p>I have shown that at the origin $O=(0,0,0,0)$, $$ \frac{\partial\tilde g_{ab}}{\partial\tilde x^c}=0 $$</p> <p>Then I am asked what is the further conditions on the $\tilde x^a$ that must be satisfied for them to be l...
g15319
[ 0.08510614931583405, 0.015057277865707874, -0.01676636002957821, -0.03316139057278633, 0.07763922214508057, 0.015671422705054283, 0.0852462574839592, 0.001302502816542983, -0.04904746264219284, 0.008099807426333427, -0.010265421122312546, 0.06106007844209671, -0.036503732204437256, -0.0285...
<p>Does blue filtered white light have a certain wavelength, or is this highly dependent on the filter and source of light?</p>
g15320
[ -0.0360238179564476, -0.028298521414399147, 0.02256786823272705, -0.010588280856609344, 0.052333783358335495, -0.030083293095231056, 0.0011425756383687258, -0.01710718311369419, -0.005115009378641844, -0.022687319666147232, 0.03508865088224411, 0.03767499700188637, 0.008809252642095089, 0....
<p>Suppose that you have a signal source, a set of point-transducers, and a handful of moderately powerful DSPs. Is it possible to construct an arrangement of the transducers such that the original signal propagates within a given region, but is absent or significantly attenuated outside of that region?</p> <p>The obv...
g15321
[ 0.014548512175679207, 0.03639449179172516, 0.004884425085037947, -0.0358613096177578, -0.04723286256194115, -0.05244943127036095, -0.002477033529430628, 0.029798174276947975, -0.023667888715863228, -0.033162496984004974, 0.012964356690645218, 0.03966936469078064, 0.008520460687577724, 0.02...
<p>Let's have the Dirac free lagrangian: $$ L = \bar {\Psi} (i\gamma^{\mu}\partial_{\mu} - m) \Psi . $$ I can rewrite it as $$ L = i\Psi^{\dagger}\partial_{0}\Psi - H_{d}, \quad H_{d} = \Psi^{\dagger}(-i(\hat {\alpha} \cdot \nabla ) + \beta m)\Psi , \quad \hat {\alpha} = \gamma_{0}\gamma . $$ Here $H_{d}$ is the Hamilt...
g15322
[ 0.023575959727168083, -0.04596402496099472, -0.03068412095308304, -0.06345099210739136, 0.04121703654527664, -0.042891714721918106, 0.043852053582668304, 0.02440721169114113, -0.0460464283823967, 0.005817968398332596, -0.01787450723350048, 0.0037384696770459414, -0.04124781861901283, -0.02...
<p>If light is considered as wave, then different colored light can be explained as waves of different wavelength/frequency. How colored light can be explained if light is considered as emission of photon?</p>
g15323
[ 0.04968683049082756, 0.036053501069545746, 0.012874456122517586, 0.021781131625175476, 0.05775797739624977, 0.010089402087032795, 0.012296297587454319, -0.02398800291121006, 0.022630786523222923, -0.048697296530008316, 0.0449044369161129, 0.01715087890625, 0.047676119953393936, 0.056569684...
<blockquote> <p>Scientists say rare drop in sunspot activity could cause global cooling</p> </blockquote> <p><a href="http://www.globalpost.com/dispatch/news/business-tech/science/110615/science-news-solar-flares-sunspots-global-warming" rel="nofollow">http://www.globalpost.com/dispatch/news/business-tech/science/11...
g15324
[ 0.017398778349161148, 0.0717957392334938, -0.01083277352154255, 0.07621555030345917, 0.051593076437711716, 0.015067888423800468, 0.022496094927191734, -0.019290147349238396, 0.011636639013886452, 0.0030930109787732363, 0.04189153388142586, 0.07079722732305527, 0.035273175686597824, -0.0291...
<p>I am making a circuit simulation program, and I am not sure how to simulate the behavior of Diodes.</p> <p>Take this circuit:<br> &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;...
g15325
[ -0.011707182042300701, -0.028180237859487534, -0.030463073402643204, -0.003925373777747154, 0.04207352176308632, -0.05023052543401718, 0.021178828552365303, 0.002321600215509534, -0.020750928670167923, -0.0008717639138922095, -0.05374772846698761, 0.0691758394241333, 0.014697272330522537, ...
<p>Could someone explain what this sentence mean? "If the Hamiltonian changes suddenly by a finite amount, the wavefunction must change continuously in order that the time-dependent Schrodinger equation be valid"?</p> <p>I am guessing that such a change describes a square-well change? And is it saying that ${\partial ...
g15326
[ 0.02269570901989937, -0.01725408248603344, -0.01739669404923916, -0.044977203011512756, 0.00363270309753716, -0.03567476570606232, 0.05681522935628891, 0.04778256639838219, -0.036261554807424545, 0.012418429367244244, -0.022678416222333908, 0.014637415297329426, -0.030116654932498932, 0.00...
<p>I have a very practical question where I've calculated the mechanical work needed by a simple mechanical system by solving the line integral $W = \int_C \ F \ dx$. However, since I have a black spot in my brain for electrical calculations I figured I could just (considering a 1.5V 2700mAh Alkaline battery) calculate...
g15327
[ -0.021202847361564636, 0.03069404326379299, -0.0016337940469384193, 0.007391571067273617, 0.0016165082342922688, -0.024657435715198517, -0.005269747693091631, 0.0022837084252387285, -0.07660652697086334, 0.034370992332696915, -0.01780347153544426, 0.00696166604757309, -0.010193122550845146, ...
<p>This experimental Question is a result of reading a particular article on Bell violations. I addressed the e-mail below to the corresponding authors —because who knows, they might reply— but it is not specific to them, it's just that their article crystallized the Question, and perhaps someone on Physics SE can tell...
g15328
[ 0.03537097945809364, 0.01449950598180294, 0.02453526295721531, 0.01753547415137291, 0.02225121669471264, -0.06112242862582207, 0.07247760891914368, 0.045072540640830994, 0.018339896574616432, -0.007013128604739904, -0.019672485068440437, 0.04958979785442352, -0.02987581118941307, 0.0207520...
<p>How can I go about magnetizing something? Specifically, a whole bunch of BB's. I want to try this so that I could make a cheaper version of the <a href="http://www.thinkgeek.com/interests/dads/bbe8/" rel="nofollow">Bucky Balls</a> product. Even if I can't replicate Bucky Balls, it'll still be an interesting proje...
g15329
[ -0.05097595974802971, 0.06030827760696411, 0.0023600575514137745, -0.05892469733953476, 0.040808241814374924, -0.02231353148818016, -0.05075792968273163, 0.008249937556684017, -0.01557548251003027, -0.036186132580041885, -0.030303437262773514, 0.03871927782893181, 0.009038837626576424, 0.0...
<p>Relativistic gravity affects particle in motion, does it affect particle that are resting too? How? and if not could one say that the matter at 0K is not affected by gravity?</p> <p>I'm not a physicist; is just a thought and probably really naive.</p>
g15330
[ 0.05178503319621086, 0.01264692097902298, -0.005758815445005894, 0.07006043940782547, 0.05173569172620773, 0.046082738786935806, 0.022037629038095474, 0.035180121660232544, -0.033131591975688934, -0.05337643623352051, 0.008559583686292171, -0.02119528129696846, -0.02166987769305706, -0.000...
<p>for TB model when we want to go to the continuum limit in real space in magnetic field (on square lattice) we use this relation <img src="http://i.stack.imgur.com/KQx6T.png" alt="enter image description here"></p> <p>and if we expand the bracket the current operator will appear</p> <p>now i want to use this applic...
g15331
[ 0.004976038355380297, 0.04995144158601761, 0.014516489580273628, -0.0335441492497921, 0.0026355781592428684, 0.01815328747034073, 0.011148650199174881, 0.061124514788389206, 0.011453263461589813, 0.03029613569378853, -0.02610943466424942, 0.021256467327475548, -0.02454179897904396, -0.0270...
<p>Does anyone know how to get from (1) to (2) in the system</p> <p>$$ \begin{align} \mathrm{g}^{\mu\nu}_{,\rho}+ \mathrm{g}^{\sigma\nu}{{\Gamma}}^{\mu}_{\sigma\rho}+ \mathrm{g}^{\mu\sigma}{{\Gamma}}^{\nu}_{\rho\sigma} -\frac{1}{2}( {{\Gamma}}^{\sigma}_{\rho\sigma}+{{\Gamma}}^{\sigma}_{\sigma\rh...
g613
[ -0.04744459688663483, -0.05058139190077782, -0.0304378904402256, -0.004820872563868761, 0.0466131828725338, 0.017325598746538162, 0.06187933683395386, -0.011459282599389553, -0.031057333573698997, 0.023150010034441948, -0.003064156277105212, 0.12769028544425964, -0.033328816294670105, -0.0...
<p>Yes, it is weird, absurd, but I can't stop thinking that the would-be superluminal neutrino speed has been computed by an arithmetic operation (space/time) and not by direct comparison with a simultaneous light ray running in "parallel". </p> <p>So the "unspeakable", outrageous question: is the speed of light incre...
g15332
[ 0.06253484636545181, 0.06932435929775238, 0.019533846527338028, 0.005399370100349188, 0.030818738043308258, -0.04848332330584526, 0.023810572922229767, 0.02084469050168991, -0.010139890015125275, -0.03890470042824745, 0.033762432634830475, 0.026864871382713318, 0.04238845035433769, 0.04638...
<p>I am trying to learn Quantum mechanics from <a href="http://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2013/other/" rel="nofollow">MIT OCW Videos</a> about quantum mechanics. I have reached the 5th lecture. Please help me in understanding this:</p> <p>In the middle (At 32:08), the professor wrote tha...
g15333
[ 0.03294425085186958, -0.01070860680192709, -0.021509559825062752, -0.014308838173747063, 0.0027239134069532156, -0.011964280158281326, 0.06454509496688843, -0.01851644739508629, -0.050527047365903854, -0.024963941425085068, -0.009245401248335838, -0.008281093090772629, -0.014674309641122818,...
<p>This is a curious question about the way George Green could have defined his <a href="http://en.wikipedia.org/wiki/Green%27s_function" rel="nofollow">Green's function</a>. All the definitions I see have only Dirac-delta $\delta(x−x′)$ function as their source on the RHS. But the Dirac-delta was defined about a centu...
g15334
[ 0.0040477304719388485, -0.00780778331682086, 0.006628013215959072, -0.024756360799074173, 0.03594249486923218, 0.003236818825826049, 0.06098954379558563, 0.01683354191482067, -0.07393421977758408, -0.08624440431594849, -0.09073223918676376, 0.004100622609257698, 0.11499982327222824, 0.0461...
<p><img src="http://i.stack.imgur.com/3Nbc9.jpg" alt="http://www.ux1.eiu.edu/~cfadd/1360/30MagSrcs/Images/FigP30.08.jpg"></p> <p>In calculating the magnetic field created by this current at the center point of the loop using <a href="http://en.wikipedia.org/wiki/Biot%E2%80%93Savart_law" rel="nofollow">Biot-Savart</a> ...
g15335
[ 0.031490787863731384, 0.016633065417408943, -0.016926776617765427, -0.028986206278204918, 0.045678868889808655, 0.00030310076544992626, 0.02015763893723488, 0.04124896228313446, -0.06445380300283432, 0.019101660698652267, -0.04866651073098183, 0.009169007651507854, -0.0069098640233278275, ...
<p><img src="http://i.stack.imgur.com/zuU5y.png" alt="Text Book Cut Out"></p> <p>I am trying to understand the procedure to setup differential equations from a block diagram. The enclosed example is about the attitude control of a satellite. The ultimate goal is to find a state-space system representation of the model...
g15336
[ 0.023178705945611, 0.0018635101150721312, -0.01987322047352791, 0.01410337258130312, 0.03142739459872246, -0.03784901276230812, 0.04288650304079056, -0.01563071459531784, -0.0033221289049834013, 0.0116189643740654, -0.0373774878680706, 0.038175273686647415, 0.0928480327129364, -0.009439911...
<p>According to quantum mechanics, energy of a state is uncertain within a small range in hydrogen atom. But we also know that energy of a state is quantized which is contradictory to the first. Which one is correct?</p>
g15337
[ 0.0171278677880764, 0.015174629166722298, -0.013699316419661045, 0.04287482798099518, -0.011037776246666908, 0.00296581257134676, -0.10432810336351395, -0.002277445513755083, -0.03865321725606918, -0.023309310898184776, 0.0028624788392335176, 0.016743116080760956, -0.04593313857913017, -0....
<p>Since the magnetic force is a no work force, $dW=\vec F\cdot d\vec r=0$ for $\vec F(\vec r)=q(\vec v(\vec r) \times \vec B(\vec r))$, therefore $\oint \vec F \cdot d\vec r=0$ by Stoke's theorem. Therefore, $\vec\nabla \times \vec F=0$. If this conclusion is true then expanding $\vec\nabla\times[\vec v(\vec r) \times...
g15338
[ 0.004277362022548914, 0.060923703014850616, 0.013016352429986, -0.0012975485296919942, 0.06322832405567169, -0.0186262559145689, 0.04305393993854523, -0.014948895201086998, 0.007923778146505356, 0.022296693176031113, -0.03222643956542015, -0.044827599078416824, -0.06334788352251053, -0.018...
<p>I'm working on a simulation of water drops falling into a pool. I'm specifically interested in the waves generated by the impact of the drops. In order to calculate the vertical motion of the waves, I believe that I need to know the "stiffness" and damping constants of water.</p> <p>I'm wondering if anyone can give...
g15339
[ 0.04565177485346794, -0.01570657268166542, -0.0140873733907938, -0.03818049281835556, 0.02548011764883995, 0.058113887906074524, 0.06451036781072617, 0.003830419620499015, -0.05333857610821724, 0.005909489002078772, -0.045068543404340744, 0.02389882318675518, -0.0038635858800262213, 0.0525...
<p>Imagine you fill up a barrel with water (or any other liquid) dig a small hole at the top and place a sufficiently large straw in it, so that there is no pressure loss or anything. Then you start to pour water in the straw. Is there a critical height at which the pressure at the level of the barrel is so big it woul...
g15340
[ 0.04613572359085083, 0.0223019290715456, 0.012184340506792068, -0.004732663277536631, -0.001823919010348618, 0.018260397017002106, -0.015463348478078842, 0.032742951065301895, -0.06133735552430153, -0.01471625454723835, -0.035681210458278656, -0.05724260210990906, -0.01386312860995531, -0....
<p>It can be proved that the size of an initial volume element in phase space remain constant in time <strong>even for time-dependent Hamiltonians</strong>. So I was wondering whether it is still true even when the system is dissipative like a damped harmonic oscillator? </p>
g15341
[ 0.07149851322174072, 0.000873297278303653, 0.03170166164636612, -0.02912529744207859, -0.03539350628852844, 0.0004747255297843367, 0.03014981932938099, 0.02404773235321045, -0.05882047116756439, 0.0014193222159519792, -0.034548450261354446, 0.005193732678890228, -0.05051356554031372, 0.024...
<p>I just came up with a question, When a battery is connected to a circuit, the current first suddenly peaks up and slowly goes down to a steady value. Why is it so? I have not actually observed this, but this question has been asked in exams, so it should be that way I hope.</p>
g15342
[ 0.07770904153585434, -0.011429041624069214, -0.004860729444772005, 0.012457042001187801, 0.0644662082195282, 0.017500394955277443, 0.03987109288573265, 0.055416177958250046, -0.042638570070266724, 0.006405749823898077, -0.04736786335706711, 0.06365650147199631, 0.007620177697390318, 0.0338...
<p>Or are they in all subshells??</p>
g15343
[ 0.003577033756300807, 0.017956281080842018, 0.0034399488940835, -0.00870033260434866, 0.038942039012908936, 0.01378567237406969, -0.023497633635997772, -0.06636200845241547, -0.015602950938045979, -0.011733011342585087, -0.03964945301413536, 0.02719130367040634, -0.04125989228487015, 0.016...
<p>Anti-de Sitter $AdS_n$ may be defined by the quadric $$-(x^0)^2-(x^1)^2+\vec{x}^2=-\alpha^2\tag{1}$$ embedded in ${\mathbb{R}^{2,n-1}}$, where I write ${\vec{x}^2}$ as the squared norm ${|\vec{x}|^2}$ of ${\vec{x}=(x^2,\ldots,x^n)}$. Now, I don't quite understand how is it justified that the topology of this space i...
g15344
[ 0.0224884245544672, 0.009467598050832748, -0.060992080718278885, 0.024785365909337997, 0.006245356053113937, -0.04012100771069527, 0.06646838784217834, 0.0024303270038217306, -0.013728545047342777, 0.03798583149909973, -0.03390767425298691, 0.039228253066539764, 0.06881315261125565, 0.0445...
<p>I'm puzzeled by a statement in <a href="http://pdg.lbl.gov/2013/reviews/rpp2012-rev-bbang-cosmology.pdf" rel="nofollow">Big Bang Cosmology</a>-review about the reheating phase subsequent to the exponential expansion during inflation: </p> <blockquote> <p>In this reheating process, <strong>entropy has been created...
g15345
[ 0.031342290341854095, 0.015008727088570595, -0.01352387573570013, -0.009855331853032112, 0.02855054661631584, 0.004273285157978535, -0.03680524230003357, 0.03810088336467743, -0.064869225025177, 0.02565966360270977, 0.005007095634937286, 0.017371511086821556, 0.044219695031642914, 0.003299...
<p>In chapter 15.2 of Peskin, the comparator is defined, as some object $U\left(y,\,x\right)$ which transforms as: $$ U\left(y,\,x\right) \mapsto V\left(y\right) U\left(y,\,x\right) \left[V\left(x\right)^\dagger\right] $$</p> <p>where $V\left(x\right)\in SU\left(2\right)^{\mathbb{R}^4}$.</p> <p>This object is introdu...
g15346
[ 0.00549271609634161, -0.02604137919843197, -0.028575090691447258, -0.06199256703257561, 0.05733974650502205, 0.018529297783970833, 0.06323736906051636, 0.052442993968725204, 0.021413713693618774, -0.04506058245897293, -0.06808611005544662, 0.02447127178311348, -0.0031537238974124193, 0.016...
<p>At room temperature, play-dough is solid(ish). But if you make a thin strip it cannot just stand up on it's own, so is it still solid?</p> <p>On a more general note, what classifies or differentiates a solid from a liquid?</p>
g15347
[ 0.061590228229761124, -0.006384482607245445, -0.01437721960246563, -0.028960565105080605, -0.02900589443743229, 0.020991811528801918, 0.008114312775433064, -0.02034703828394413, 0.005839159246534109, -0.06257285922765732, -0.03871950879693031, -0.04113784059882164, -0.018128233030438423, 0...
<p>Could someone sketch me what <a href="http://www.google.com/search?as_q=string+theory&amp;as_epq=algebraic+geometry" rel="nofollow">algebraic geometry has to do with string theory</a>? Are there other mathematical disciplines that are interwoven with string theory?</p> <p>I'm aware of <a href="http://math.stackexc...
g15348
[ 0.084385946393013, 0.06040428578853607, 0.011335385031998158, -0.03931858390569687, 0.025605978444218636, -0.0019390861270949244, 0.026470554992556572, -0.03348160907626152, -0.010822257958352566, -0.03171171247959137, -0.02259139157831669, 0.0018855930538848042, 0.09761696308851242, 0.011...
<p>Having two current carrying (currents $I'$ and $I$) wires of length $a$ parallel to the $z$-axis, one with end points $(0,0,0)$ and $(0,0,a)$ and one from $(a,0,0)$ to $(a,0,a)$, I'm looking for the force on the second one due to the first one. Here is my problem:</p> <p>I know I'm suppose to get (which I get by fi...
g15349
[ 0.047413717955350876, -0.0006881680455990136, -0.01735837385058403, -0.08373934775590897, 0.052147891372442245, -0.02411624789237976, 0.019507601857185364, -0.02416170947253704, -0.07111859321594238, 0.021065019071102142, 0.004469568841159344, 0.029047992080450058, -0.09334596246480942, -0...
<p>I recently came across an interesting explanation of diffraction through an aperture which does not use Huygens' Construction but instead relies on Heisenberg's Uncertainty Principle:</p> <blockquote> <p>The Uncertainty Principle states that trying to pin a particle down to a definite position will create uncerta...
g15350
[ 0.026975009590387344, 0.02362593449652195, 0.0033161486499011517, 0.02764127403497696, -0.005343073979020119, 0.051361311227083206, 0.07100532948970795, 0.03546581044793129, 0.017824167385697365, -0.023336801677942276, 0.010514557361602783, -0.045388590544462204, -0.027517858892679214, -0....
<p>I have a basic question: if we use 1d string to replace 0d particle to gain insight of nature in string theory, and advanced to use 2d membranes, can we imagine that using $3$- or $n$-dimensional blocks/objects/branes as basic units in physics theory? Where is the end of this expansion?</p>
g15351
[ 0.020540371537208557, 0.05215836688876152, 0.009784495458006859, -0.020813394337892532, 0.0050247726030647755, 0.032214030623435974, 0.028172623366117477, 0.010126308538019657, -0.0045620109885931015, -0.05012112483382225, 0.018747419118881226, 0.040594879537820816, 0.02066926471889019, 0....
<p>I want to learn some <a href="http://en.wikipedia.org/wiki/Quantum_field_theory_in_curved_spacetime" rel="nofollow">QFT in curved spacetime</a>. What papers/books/reviews can you suggest to learn this area? Are there any good books or other reference material which can help in learning about QFT in curved spacetime...
g15352
[ 0.040530186146497726, 0.010755262337625027, -0.0101928124204278, -0.05058034136891365, 0.0077667441219091415, 0.00684416713193059, -0.039343658834695816, -0.055865172296762466, 0.00268191029317677, 0.00739080086350441, 0.007252255454659462, 0.0320877805352211, 0.03940306976437569, -0.00603...
<p>What is the reason why quarks moving freely in confined nucleus do not radiate energy like any accelerated charge banging around in a bag? If the answer is that they have distinct energy levels like electrons in an atom, then why must quarks have distinct quantum numbers, that would allow them to have the same energ...
g15353
[ 0.032449714839458466, 0.08709321171045303, -0.0007084014941938221, 0.006453561596572399, 0.007807908579707146, 0.04889915511012077, -0.016454139724373817, -0.000020510162357822992, -0.012854060158133507, -0.04837106540799141, 0.01760883256793022, 0.008761773817241192, -0.03283453360199928, ...
<p>Continuous <a href="http://en.wikipedia.org/wiki/Fourier_transform" rel="nofollow">Fourier transform</a> vs. <a href="http://en.wikipedia.org/wiki/Discrete_Fourier_transform" rel="nofollow">Discrete Fourier transform</a>. Can anyone tell me what the difference is physics-wise? I know the mathematical way to do both,...
g15354
[ 0.05632865056395531, -0.00513452710583806, -0.006186190526932478, -0.03591268137097359, 0.059322815388441086, -0.05070360004901886, 0.01669425517320633, 0.030880963429808617, -0.09101296961307526, -0.09823259711265564, 0.014631517231464386, -0.03391331806778908, 0.06092815846204758, -0.019...
<p>Let be $B$ an operator and $\left|\Psi\right&gt;$, $\left|\Phi\right&gt;$ two states (not necessarily equals). </p> <p>What is the meaning of a matrix element $\left&lt;\Psi\right| B \left|\Phi\right&gt;\neq 0$ for $\left|\Psi\right&gt; \neq \left|\Phi\right&gt;$ ? Can i think that this matrix element isn't zero du...
g15355
[ 0.017776500433683395, 0.03800525143742561, 0.0012563830241560936, -0.039979834109544754, 0.058488018810749054, -0.010781180113554, 0.005904716905206442, 0.04652628302574158, 0.025240479037165642, -0.05043794587254524, -0.025566281750798225, 0.06550288200378418, -0.03152170777320862, -0.010...
<p>Say now I have an arbitrary field strength tensor $F$, and I want to boost it according to a Lorentz transformation matrix $(\Lambda)$</p> <p>The transformation is given by $$ F^{'\mu \nu} = \Lambda^{\mu}_{\;\alpha} \Lambda^{\nu}_{\;\beta} F^{\alpha\beta} $$</p> <p>The question is, how do I actually calculate th...
g15356
[ -0.016715746372938156, 0.014268102124333382, -0.023120680823922157, -0.05018305405974388, 0.030109096318483353, -0.029058897867798805, -0.04818037152290344, 0.05455808341503143, -0.01921122334897518, -0.0004233715299051255, -0.08064984530210495, 0.019421035423874855, 0.020155517384409904, ...
<p>The coarse grained fluctuations of the Neel order parameter in the half integer spin anti-ferromagnetic Heisenberg model is described by the O(3) non-linear sigma model with a strange berry phase term.</p> <p>See for example : Eq-2 in <a href="http://arxiv.org/pdf/cond-mat/0311326.pdf" rel="nofollow">http://arxiv.o...
g15357
[ 0.01984807848930359, -0.017578763887286186, 0.011891021393239498, 0.013727789744734764, 0.04109415039420128, 0.0004698200209531933, 0.01762625016272068, 0.026241904124617577, -0.006569720339030027, 0.01399265043437481, -0.028671815991401672, 0.02174001932144165, 0.035724807530641556, -0.01...
<p>I have some fog in my head and a rather simple question for you: </p> <p>When the sign of the wave function is representated on orbitals, what is this sign? I mean is it the sign of the <strong>real part</strong> of the wave function only? Or is it the sign of the complex wave function?</p> <p>Thanks if you have a...
g15358
[ -0.05075566843152046, -0.0051447441801428795, -0.004023794084787369, -0.014936922118067741, 0.01820870116353035, 0.016906417906284332, 0.02535860426723957, 0.06773756444454193, 0.04512466490268707, -0.026330089196562767, -0.03289789333939552, 0.02273649349808693, 0.05954043194651604, -0.00...
<p>I am supposed to find the wave speed of a standing wave from a graph of frequency vs linear density, and I'm not exactly sure how. Any help would be great, thanks.</p>
g15359
[ 0.08389229327440262, 0.05253498628735542, 0.008520165458321571, -0.03255344182252884, 0.06266959011554718, -0.07495932281017303, -0.006489421706646681, 0.0032380458433181047, -0.026302065700292587, -0.02168542891740799, 0.026946241036057472, -0.011879024095833302, 0.006062629632651806, -0....
<p>It might seem logical to presume that the exact state of the world around us could have been predicted given a big enough computer to analyse all the particle's interactions and what not. Determinism seems to be logical.</p> <p>Then comes quantum computing. Since a collection of entangled qubits are only coherent w...
g15360
[ 0.02485196478664875, 0.039699021726846695, 0.011033611372113228, -0.010312086902558804, 0.01924946717917919, 0.03372685983777046, 0.02367989718914032, 0.02165144868195057, -0.026697395369410515, -0.07492270320653915, -0.03205648809671402, -0.007752354722470045, 0.07152397185564041, 0.04806...
<p>We all know that if an electric field is applied across an isolated conductor, then charges are induced at either surface such that the net electric field inside becomes zero.</p> <p>Now if the applied electric field is so strong that there are not sufficient free electrons in the metal to move and cause the requir...
g474
[ 0.021555311977863312, 0.02532183937728405, 0.003493733238428831, 0.011003962717950344, 0.05438777431845665, 0.0580679252743721, -0.027421221137046814, 0.031245853751897812, 0.008920894004404545, -0.011510612443089485, -0.08863110840320587, 0.00906472560018301, -0.04238489270210266, -0.0449...
<p>I think that bob maybe already, at least partially, has answered my following question: "Is it true or false that the <em>frequency</em> of a photon is not related to the <em>change</em> of its frequency caused by gravitational effects?"</p> <p>bob gave the answer: "While you are correct that the size of the redshi...
g15361
[ 0.02417115680873394, 0.021927783265709877, 0.01703619584441185, 0.02337772212922573, 0.019268643110990524, 0.02417866513133049, 0.04984327778220177, 0.0007300886791199446, -0.02816852554678917, -0.033088017255067825, 0.035677630454301834, -0.023416893556714058, 0.04383966326713562, 0.05979...
<p>The <a href="http://en.wikipedia.org/wiki/Field_electron_emission#Equations_for_cold_field_electron_emission_.28CFE.29" rel="nofollow">Fowler-Nordheim equation</a> describes the emission current accurately in a specific temperature and electric field range [1] and the maximum valid field is about 11 V/nm. Is there a...
g15362
[ 0.001657067216001451, -0.004139131400734186, 0.012163483537733555, -0.0011853068135678768, 0.022546254098415375, -0.041312020272016525, -0.03391837701201439, 0.029838135465979576, -0.038801342248916626, 0.026587186381220818, 0.03485223650932312, 0.04807379096746445, 0.020311256870627403, -...
<p>Soon, I am going to write my master thesis in theoretical physics. I assume there, and later on in my career, I will have to do more serious numerics than I did up to this point. That's why I want to find out:</p> <p><strong>What programming languages are available for doing numerics in theoretical physics? What a...
g15363
[ 0.02023296244442463, 0.025325924158096313, 0.03108932264149189, -0.01903885416686535, -0.03947681561112404, -0.049867406487464905, -0.018331995233893394, 0.04708642512559891, -0.04739364981651306, -0.04668577015399933, 0.021115083247423172, -0.011169105768203735, 0.024163443595170975, 0.00...
<p>In the late 80's and early 90's, Smalley and others made claims that the C60 fullerene bearing icosahedral symmetry was the most spherical molecule known, and perhaps the most spherical that could exist. While it makes sense to me that the smallest member of the 60n^2 isocahedral family of buckyballs would be the m...
g15364
[ 0.034458909183740616, 0.03039305843412876, -0.004422757774591446, -0.02628951147198677, 0.02071794867515564, 0.0016240897821262479, 0.026366975158452988, -0.046246487647295, -0.021293342113494873, -0.00385117344558239, 0.02359054982662201, -0.05619696527719498, 0.08996783196926117, 0.03234...
<p>So I learned that after a measurement of, lets say the position of the wavefunction of a particle is made, if another measurement of the position of the particle is made right away, you should get the same result because the wavefunction has collapsed.</p> <p>How can you tell the difference between the observer mea...
g15365
[ 0.03206423670053482, -0.03078962117433548, 0.006217820104211569, -0.03828859329223633, 0.058039747178554535, 0.014966817572712898, 0.05675318464636803, 0.01283579133450985, -0.013034731149673462, -0.03755306079983711, -0.0614415667951107, -0.01596694439649582, 0.02117186412215233, 0.073304...
<p>Is it possible to measure the spin of a single electron? What papers have been published on answering this question? Would the measurement require a super sensitive SQUID, Superconductive Quantum Interference Device?</p>
g15366
[ -0.05325546860694885, 0.03721626102924347, 0.0020577486138790846, -0.03573376685380936, 0.04679762199521065, -0.011161443777382374, 0.014145111665129662, 0.07147135585546494, 0.038359660655260086, -0.003495215903967619, -0.07017456740140915, 0.030901307240128517, -0.043234292417764664, -0....
<p>In the path integral approach to Quantum Mechanics, can two distinctly different paths of the possible infinite paths have the same phase, i.e can there be a <a href="http://en.wikipedia.org/wiki/Bimodal_distribution" rel="nofollow">bimodal distribution</a> of the phases associated with each path? And Why?</p>
g15367
[ 0.02251281589269638, 0.03545313701033592, 0.010167211294174194, -0.04372911527752876, 0.034674324095249176, -0.027865730226039886, -0.029846562072634697, 0.02188635990023613, -0.021374179050326347, 0.007774222642183304, 0.007132872939109802, -0.055306557565927505, -0.029184944927692413, 0....
<p>I have been trying to interpret a<a href="http://en.wikipedia.org/wiki/Poincar%C3%A9_map" rel="nofollow"> Poincare Map</a>. The Hamiltonian for the system is</p> <p>$$H=\frac{1}{4m}\left(p_r^2+p_z^2\right)+m\omega_\perp^2 r^2 +m\omega_z^2 z ^2+ \frac{q^2}{8\pi\epsilon_0\sqrt{r^2+z^2}}.$$</p> <p>So, we have a 4D sp...
g15368
[ 0.00877068005502224, -0.010758358053863049, -0.02354319393634796, -0.024404680356383324, -0.009259010665118694, -0.029894094914197922, 0.04090268164873123, 0.019153304398059845, -0.004820382688194513, 0.03464842960238457, 0.0029867205303162336, 0.01977272517979145, -0.009218149818480015, -...
<p>I have read Luboš Motl's blog and he says in QG electrons must be composite and have structure because QG says there can be no point like particles and everything above the Planck size can be resolved but under it can't so electrons bring above the Planck size must be composite? Does all QG theories say electrons mu...
g15369
[ -0.028499212116003036, 0.04338293895125389, -0.0014268470695242286, 0.004684376064687967, 0.015140211209654808, 0.01560059655457735, -0.03894039988517761, -0.039501287043094635, -0.02085205167531967, -0.03631005063652992, -0.0005570923094637692, -0.024083135649561882, -0.03855377435684204, ...