question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>Every physics book I've come across defines a vector as an n-tuple of numbers that can be combined via an inner product that's invariant to rotations. </p>
<p>Is it possible to instead define a vector via an algebraic operation that's invariant to translations, or is there something unique about the invariance of a... | g15836 | [
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<p>Can a neutrino act as a virtual particle between two electrons to mediate electron-electron fermonic interaction analogous to how a photon acts as a virtual particle between two electrons to mediate a bosonic electron-electron interaction?</p>
<p>What would the Lagrangian look like for an electron-electron interact... | g15837 | [
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<p>I can't seem to figure out how to derive the coordinate representation of the $a_+$ ladder operator in quantum mechanics.</p>
<p>I know that $a_-$ is $\sqrt{\frac{1}{2mwh}} (mwx + i\dot{p}) $ in which where I can substitute $i\dot{p}$ to make the representation:</p>
<p>$$\sqrt{\frac{1}{2mwh}} (mwx + \hbar \frac{d}... | g15838 | [
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<p>I'm sure this has caused many people headaches.</p>
<p>First, is there a metric $(-+++)\leftrightarrow(+---)$ convention conversion chart where many common expressions are listed? Thank you in advance for sharing.</p>
<p>Second, as an example, I read that in $(+---)$ we have the fermion propagator
$$\frac{i}{\gamm... | g15839 | [
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<p>Consider a particle of mass $m$ in $6$ dimension. Its coordinate w.r.t. origin $\left(0,0,0,0,0,0\right)$ is given as $\left(x,y,z,\dot{x},\dot{y},\dot{z}\right)$. If we denote $r = \sqrt{x^2+y^2+z^2}$, then which of the following two is the kinetic energy of this particle:</p>
<ol>
<li><p>$T = \frac{1}{2}m\left(\d... | g15840 | [
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<p>I am supremely confused when something has spin or when it does not. For example, atomic Hydrogen has 4 fermions, three quarks to make a proton, and 1 electron. There is an even number of fermions, and each fermion has a 1/2 spin. Since there are an even number of fermions, the total spin value is an integer. This s... | g243 | [
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<p>I just read that, with respect to a stationary tiny cube, suspended in a fluid, that has a negligible weight and dimensions: </p>
<blockquote>
<p>Pressure is the same in every direction in a fluid at a given depth, if it weren't the fluid would start to move.</p>
</blockquote>
<p>This made sense to me the first ... | g15841 | [
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<p>How do we define the longitudinal relaxation time and transverse relaxation time?</p> | g15842 | [
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<p>Given a timelike reference worldline (not necessarily geodesic), we can define light-cone coordinates $\tau^+$ and $\tau^-$ so that the 3-D hypersurfaces of constant $\tau^+$ are past light cones of events on the reference worldline, the value of $\tau^+$ being reference proper time. Similarly $\tau^-$ for future li... | g15843 | [
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<p>From <a href="http://techcorr.com/services/Inspection-and-Testing/Ultrasonic-Shear-Wave.cfm" rel="nofollow">this explanation</a>, I learn that sound is refracted according to Snell's Law upon passing a border between materials of different sound speed. </p>
<p>I also learn that upon passing the border, a <em>mode c... | g15844 | [
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<p>With $[x,p_x]=i\hbar $, how to determine the form of the operator $p_x$?</p> | g15845 | [
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<p>In a longitudinal wave, why is there zero particle displacement at a compression or rarefaction and maximum displacement at a point pi/2 from it? Shouldn't it be the other way round?</p> | g15846 | [
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<p>Elementary particles can be grouped into spin-classes and described by specific equations, see below: </p>
<p><strong>Is there a general Lagrangian density from which all these equations can be derived?</strong></p>
<p><strong>A Lagrangian that allows for all types of spin, but after some gauge transformation sett... | g15847 | [
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<p>Recently, I have been studying a quantum protocol for the "Hidden Matching" problem that makes use of states that can be expressed as</p>
<p>$|\psi\rangle=\frac{1}{\sqrt{n}}\sum_{i=1}^n (-1)^{x_i}|i\rangle$,</p>
<p>where $x_i\in \{0,1\}$ and $n$ is a power of 2. Note that instead of an $n$-level system we can cons... | g15848 | [
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<p>What would be good introductory and follow-up references to understand the close ties between physics and geometry.</p>
<p>I'm a retired engineer with the math background to handle Shankar's Principles of Quantum Mechanics, but like most engineers my era, I know little of the fundamentals of set theory, group theor... | g15849 | [
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<p>I've been looking at the literature on quantizing the bosonic string, and I noticed that there was a change made in the definition of the BRST current around 1992. However, I haven't found any illuminating discussion about why the change was made.</p>
<p>In Green-Schwarz-Witten (and other mathematics and physics l... | g15850 | [
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<p>We knows that in a critical system and self organized criticality we have long range interaction due power law decay in correlation. Is this fact equivalent to the butterfly effect? </p> | g15851 | [
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<p>Slightly inspired by <a href="http://physics.stackexchange.com/q/53385">this question</a> about the historical origins of the Born rule, I wondered whether quantum mechanics could still work without the Born rule. I realize it's one of the most fundamental concepts in QM as we understand it (in the Copenhagen interp... | g15852 | [
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<p>Newton spent much of his life in the fruitless pursuit of alchemy, but along the way discovered and worked-out much else that was real, practical science. And I was thinking about why it is that we can safely dismiss anyone who claims to have invented a perpetual motion machine, but then I thought: even when we fail... | g15853 | [
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<p>I'm starting to learn about gauge theories and Goldstone bosons. What does it mean for a group to be gauged?</p> | g15854 | [
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<p>I'm reading a book on the finite element method. Specifically I'm looking at the background material where they are discussing potential energy, equilibrium, and the Rayleigh–Ritz method.</p>
<p>The book claims that potential energy is equal to strain energy + work potential energy. I see that strain energy is like... | g15855 | [
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<p>The restoring force of a spring is F(x) = -k(x-x0)exp(-t/T) where k and T are constants, x is the position of a mass on the spring, and x0 is the position of equilibrium of the spring.</p>
<p>How do you find the potential energy of the mass-spring system?</p>
<p>How do you determine the amount of energy lost per t... | g15856 | [
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<p>I've heard about the <a href="https://en.wikipedia.org/wiki/Fine-tuned_Universe" rel="nofollow">fine-tuning principle</a> and how if the fundamental constants of the Universe were changed even a slight bit, life could not exist as we know it.</p>
<p>However, study on this subject seems to only have really started a... | g15857 | [
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<p>Although I doubt somewhat whether this question is really appropriate for this site, I hope it gets answered anyways. I guess, what I'm wondering is:</p>
<ol>
<li><p>How does one get to work as a theoretical physicist and - probably more importantly - what do theoretical physicist actually do all day long?</p></li>... | g86 | [
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<p>Maybe my question will seem stupid, but I am not a physicist so I have some problems understanding a classic Newtonian experiment: in the <a href="http://en.wikipedia.org/wiki/Bucket_argument">bucket experiment</a>, why does he have to introduce the absolute space in order to explain the accelerated motion of water ... | g15858 | [
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<p>I have an exercise for Yang-Mills theory. I can't find answer anywhere.</p>
<blockquote>
<p><em>Derive equations of motion for the Yang-Mills theory with the gauge group $SU(2)$ interacting with $SU(2)$ doublet of scalar fields.</em></p>
</blockquote>
<p>I don't even know how to derive EOM for Lagrangian here. A... | g15859 | [
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<p>What kind of rocket would be needed to send 100 gr of mass to outer space? </p>
<p>The mass can be moulded in any shape, but it would need not raise above 40 °C of temperature during the process.</p> | g15860 | [
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<p>The term 'tensor rank' is sporadically used in the mathematical literature to denote the minimum number of simple terms (i.e. tensor products of vectors) needed to express the tensor. This is analogous (and equivalent) to the usual and prevalent notion of <a href="http://en.wikipedia.org/wiki/Rank_%28linear_algebra%... | g15861 | [
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<p>This operator identity showed up in a course I was taking, and it was given without proof.</p>
<p>$$[L^2,[L^2,\vec{r}]]=2 \hbar ^2 \{ L^2, \vec{r}\}$$</p>
<p>The curly brackets denote the anticommutator, $AB+BA$. The $\vec{r}$ operator is the position operator. The $L^2$ operator is given by: </p>
<p>$$L^2 = -\hb... | g15862 | [
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<p>while studying some material on ballistic trajectories (the basic gravity-only parabola), I've tried to come up with closed-form expressions for another case, where in addition to gravity we add a constant force on the x-direction:</p>
<p><img src="http://i.imgur.com/cmVxMla.png?1" alt="diagram"></p>
<p>With a fir... | g15863 | [
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<p>In Arnold Neumaier's nice answer to this question:</p>
<p><a href="http://physics.stackexchange.com/questions/3941/the-energy-spectrum-in-quantum-field-theory#">The energy spectrum in quantum field theory</a></p>
<p>it is remarked that</p>
<p>'If there is a mass gap (i.e., if no representation of tiny positive ma... | g15864 | [
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0.... |
<p>In (3.87, page. 53) Peskin and Schroeder write $$\psi(\vec{x}) = \int\frac{d^{3}p}{(2\pi)^{3}} \frac{1}{\sqrt{2E_{\vec{p}}}} e^{i\vec{p} \cdot \vec{x}} \sum_{s=1,2} (a_{\vec{p}}^{s}u^{s}(\vec{p}) + b_{-\vec{p}}^{s}v^{s}(-\vec{p})) $$ and then compute</p>
<p>$$[\psi(\vec{x}),\psi^{\dagger}(\vec{y})]=\int\frac{d^3p ... | g15865 | [
0.018741797655820847,
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0.06596409529447556,
0.015130573883652687,
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<p>Ignoring quantum effects, what are the dynamics of an electrically charged particular placed with zero initial momentum in an oscillating electromagnetic field, e.g. light?</p> | g15866 | [
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<p>Is the universe infinite? Or is it finite?</p>
<p>If it is infinite,it's very difficult to imagine an endless space(though not impossible).</p>
<p>But if it's finite, the idea that we can't go beyond a certain space just creeps me out.</p>
<p>So, what is it actually? </p> | g62 | [
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<p><a href="http://en.wikipedia.org/wiki/Quantum_entanglement">Quantum entanglement</a> is the norm, is it not? All that exists in reality is the wave function of the whole universe, true? So how come we can blithely talk about the quantum state of subsystems if everything is entangled? How is it even possible to consi... | g15867 | [
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<p>A child tosses a ball directly upward. Its total time in the air is T. Its maximum height is H. What is its height after it has been in the air a time T/4? Neglect air resistance.</p>
<p>Ok so I know that there is no x-component to the velocity: </p>
<p>$$D=v_0 t+\frac{1}{2}at^2$$
$$\frac{1}{2}D=H$$ so, $$\frac{1... | g15868 | [
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<p>I'm having trouble with the following exercise:</p>
<p>Some point defects (impurities, holes, etc.) in semiconductors can trap an electron in a localized state with energy $E_{1}$ and spin $-1/2$. A second electron captured by the same defect would face the coulombian repulsion of the first electron and its energy... | g15869 | [
0.037878260016441345,
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0.04203733801841736,
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<p>For a moment, assume that travel at/over the speed of light is possible, and we fire a laser in front of us, what happens to the light emitted from the laser?</p>
<p>Would the photons scatter, or would the light only move at light-speed (that is to say, without a visible source).</p>
<p><strong>Edit:</strong>
To a... | g15870 | [
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0.051896609365940094,
-... |
<p>What happens with the spin in Andreev reflection process ? The simple Bogoliubov - De Gennes equation for hole and electron does not contain information about the spin. I know there are some generalizations to spin dependent formalism but I can't find good refrence. Can You recommend good papers/books about spin dep... | g15871 | [
-0.01254439726471901,
0.00805574655532837,
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<p>I would like to know how the signals for remote controlled cars, radios, etc.. That use radio waves are told apart from each other. I know that the radio waves are modulated to encode data and the frequency or amplitude are changed, so then the waves are propagated through the air and received at another location vi... | g15872 | [
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<p>I have read some paper which says that the electroweak Lagrangian includes these terms like
$\bar{\psi} \gamma_a\gamma_5\psi$ and $\bar{\psi} \gamma_a \psi$.
They violate charge conjugation symmetry. I understand the violation of the first term, but I did not get whether the second term violates or does not violate ... | g15873 | [
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0.0635... |
<p>I think that the most successful theory of gravity is that the orbit of planet can be explained with this theory and the orbit of satellite was designed with this theory. To design an orbit of a satellite, the three of the factors of the orbit: 1) The radius, 2) The inclination angle, 3) The eccentricity, must be ca... | g15874 | [
0.013897760771214962,
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<blockquote>
<p>It is known that the period of revolution of the earth about the sun is $365.3$ days and that the semimajor axis of the earth's orbit is $1.495 \times 10^{11}$ m. An astronomer notes that the period of a distant planet is $29.7$ earth years. What is the semimajor exis of the distant planet's orbit? Ch... | g15875 | [
0.008944546803832054,
0.06437579542398453,
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<p>$$\int_{-\infty}^{\infty}\frac{\partial^2\bar{\psi}}{\partial{x^2}}\frac{\partial\psi}{\partial{x}}~dx.$$ </p>
<p>I have read that this is equal to Zero. Only problem is that what I am reading about doesn't really explain why.</p>
<p>I think it is that at positive and negative infinity the $\frac{\partial\psi}{\pa... | g15876 | [
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0.019433598965406418,
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-... |
<p>I dont know much about quantum computing except what i have read about on wiki and popsci. I have been reading about the de broglie-bohm pilot wave theory and how they describe quantum mechanics in terms of discrete particle travelling a pilot wave and it seems produce the same quantum mechanical statistics as the c... | g488 | [
0.0066353376023471355,
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0.014942729845643044,
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0.0019551143050193787,
... |
<p>A strange particle, $X$, decays in the following way: $X → π^– + p$. State what interaction is involved in this decay.</p>
<p>I know the answer to be weak interaction, but why is it weak interaction? What is the reasoning? Why could it not be a strong interaction? Is it merely because the particle is a strange part... | g15877 | [
0.06467065960168839,
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0.028127942234277725,
0.001178780454210937,
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<p>The potential difference across a voltaic cell varies with temperature. But my question is whether the voltage increases or decreases as temperature rises. According to the Nernst equation, the two are inversely proportional, however if one were to use Gibb's Free Energy equation, as temperature increases, so does t... | g15878 | [
0.06066739559173584,
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0.05855732411146164,
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0.018227... |
<p>I was recently shown a pretty <a href="http://www.iflscience.com/space/biggest-misconceptions-about-universe-explained">cool video about common cosmological misconceptions</a>. It got me reviewing the different between event horizon (current distance within which we <strong><em>will see/interact</em></strong>), par... | g15879 | [
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<p>How dangerous may it be when experimenting with a parallel plate capacitor typically used in physics demonstration experiments? Take for example this one (that's what I use): <a href="http://www.ld-didactic.de/ga/5/544/54422/54422de.pdf" rel="nofollow">http://www.ld-didactic.de/ga/5/544/54422/54422de.pdf</a></p>
<p... | g15880 | [
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0.033784... |
<p><strong>Context</strong>: I'm studying basic thermodynamics. My textbook has a chapter on the <a href="http://en.wikipedia.org/wiki/Clausius%E2%80%93Clapeyron_relation" rel="nofollow"><em>Clapeyron</em> equation</a> which, as a reminder, is given by the following formula:</p>
<p>\begin{equation}
\frac{dP}{dT} = \fr... | g15881 | [
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0.002179979346692562,
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0.04584420844912529,
-0... |
<p>I have the following data:<br>
Assume a man falling from a plane from a height of 370 m ($=h$) high (Straight down). The man falls into a pile of snow and creates a 1.1 m ($=d$) deep crater. The man has a mass of 88kg ($=m$) and his velocity right before hitting the snow was 45 m/s ($=v$). What is the amount of work... | g15882 | [
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0.010909728705883026,
0.01807967945933342,
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<p>What is the defining property for two quantum states to become <a href="http://en.wikipedia.org/wiki/Quantum_entanglement" rel="nofollow">entangled</a>? Is it just that the combined system cannot be in a product state? Why is this? </p> | g15883 | [
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<p>In an atom, two electrons can have the same set of $n,\ell,m$ quantum numbers as long as they have opposite spins. My introductory physics and chemistry courses have all introduced this as two electrons occupying the same energy state; however, the spins of the electrons cause splitting of the energy levels they oc... | g15884 | [
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<p>Some internet (among other) infrastructure comprises satellites, which beam communications in radio frequencies. These satellites, to ground observers, appear as very small solid angles in the sky.</p>
<p>This makes me wonder if there is significant interference between other skyward radio sources (e.g. stars (incl... | g15885 | [
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<p>I have the following general conceptual concern.</p>
<p>Think of a thin conducting loop of radius $R$ placed in the $x$-$y$-plane at $z=0$. There is a homogeneous current density $\vec{j}$ running through this loop:</p>
<p>$$\vec{j}(\vec{r})=|j|\delta(z)\delta(x^2+y^2-R^2)\frac{-y\,\vec{e}_x+x\,\vec{e}_y}{\sqrt{x^... | g15886 | [
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... |
<p>What is the difference of OAM of photons and their polarization?</p> | g15887 | [
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<p>When deriving the continuity equation in physics class for two immiscible fluids flowing in succession we used the principle of conservation of mass. My question is, shouldn't volume be conserved instead of the mass?</p>
<p>To further elaborate, assume section 1 of a pipe has cross-section area $A_1$ and section 2 ... | g15888 | [
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0.003428039839491248,
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0.0231... |
<p>I started reading Landau's Mechanics book and was having some trouble understanding the Galilean Relativity Principle.
What does Landau mean by saying space to be homogenous and isotropic and time is homogenous for an inertial observer ?
Also, how does he conclude using this that, the Lagrangian must be independent... | g15889 | [
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... |
<p>Parts of Antarctica average -127°F (-83°C). The freezing point of $\mathrm{CO_2}$ is -109.3 °F (-78.5 °C). If one could construct a large container at such a place shielded from the sun, would atmospheric $\mathrm{CO_2}$ be expected to freeze out inside the container? If so, what rate of deposition could be expected... | g15890 | [
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0.01713799685239792,
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<p>Can we use eigenstates of ANY observable as base of the Hilbert space? If we can, is this equal to the statement that those eigenstates are orthogonal to each other and normalizable?</p> | g15891 | [
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<p>The problem is as follows.</p>
<p>A searchlight casts a spot of light along the face of a horizontal wall located 100m above from the searchlight. It rotates at a constant $\omega$ of 4rads/s. Determine the magnitude of the velocity and acceleration at which the spot appears to travel across the wall at the instant... | g15892 | [
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0.024428963661193848,
0.013382130302488804,
0.05657706409692764,
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<p>I have a hydrogen atom, knowing that its Hamiltonian has been modified turning the standard potential
$$
V_{0}(r) = -\frac{Z}{r}
$$
into
$$
V(r) = -\frac{g}{r^{\frac{3}{2}}}
$$
with $g$ a positive constant.</p>
<p><strong>An upper bound to the ground-state energy is to be determined.</strong></p>
<p>I thought o... | g15893 | [
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0.03702693432569504,
-0.005567806772887707,
... |
<p>Inspired by <a href="http://physics.stackexchange.com/questions/51308/why-does-smoke-go-out-the-window-of-the-car-and-what-if-theres-wind-blowing-i">another question</a> I wanted to ask about phenomenon that I've experienced.</p>
<p>We had a van with separate trunk deprtment (similar looking one below) to transport... | g15894 | [
-0.025426751002669334,
-0.011757711879909039,
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0.03789517283439636,
... |
<p>According to my physics book, the spring constant can be calculated from knowing the potential energy, with the formula $k = W_p''(0)$.</p>
<p>I don't really understand why, and the book doesn't explain it any further. How do I know the two are equal?</p> | g15895 | [
0.086122527718544,
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/9857/what-is-an-observer-in-quantum-mechanics">What is an observer in quantum mechanics?</a> </p>
</blockquote>
<p>I'm sick of quantum physics explanations which term experiments where the outcome depend... | g75 | [
0.04337887838482857,
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0.046916503459215164,
0.02618184... |
<p>As I understand, the kinetic energy of the proton beam in a hadron collider is quite large. Can you build a energy storage system that is based on accelerating a proton beam to relativistic speeds to retrieve the energy later?</p>
<p>Here is my related question:
<a href="http://physics.stackexchange.com/questions/2... | g15896 | [
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<p>I would like to ask a question about the so-called ''Master Field''. As far as I understand, this represents a classical configuration in the large n limit (saddle point solution) but there is no systematic way to derive master fields for gauge theories. Is anybody trying to solve this problem anymore? Has the Ads/C... | g15897 | [
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<p>At the macroscopic level a simple metal file or rasp creates a large amount of friction in one direction and a much smaller amount in the opposit direction. Shark skin displays the same properties due to very fine scales.</p>
<p>Are there any materials with a surface that displays similar behaviour at a microscopic... | g15898 | [
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<p>Let $|0\rangle,...$ be the states of the harmonic oscillator. Then a squeezed state was defined as $|\xi\rangle =S(\xi)|0\rangle $, where $S(\xi):=e^{\frac{1}{2}( \xi (a^{ \dagger ^2}-a^2))}$, where $a$ and $a^{\dagger}$ are the canonical operators linked with the harmonic oscillator problem in QM.</p>
<p>Now we we... | g15899 | [
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<p>I am interested in deriving what the radial and tangential components of the acceleration vector should be for an object following an elliptical trajectory centered on the origin, in which the relation between the speed $v$ (module) is related to the distance of the object to the origin ($r$) by $v=kr^\beta$ where $... | g15900 | [
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<p>There are lots of ways to apply the mean field method to deal with the Ising model whose ground state is a ferromagnetic state. Hence, it is easy to find the order parameter named magnetization to describe the mean behavior of spin-spin interaction.</p>
<p>But, in the antiferromagnetic Ising model, the ground state... | g15901 | [
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<p>From answers to <a href="http://physics.stackexchange.com/questions/3889/is-a-normal-ordered-product-of-free-fields-at-a-point-a-wightman-field">a previous question</a>, a finite degree polynomial in the distribution $i\Delta^+(x)$, with Fourier transform $2\pi\delta(k^2-m^2)\theta(k_0)$, <em>is</em> a distribution,... | g15902 | [
0.024832708761096,
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<p>I am somehow confused by the notion of auxiliary fields, such as for example the fields F and D which appear in supersymmetry, and the notion of ghost fields which appear for example in the BRST formalism. Both kinds of fields are deemed to be not physical. </p>
<p>Can somebody once and for all in a clear cut way e... | g15903 | [
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<p>If we talk about electric heating then we have simple elements in which we apply electrical energy which gets converted into the kinetic energy of the electrons which heats it up.</p>
<p>But while cooling, we need to take away energy from those electrons doing their dances, since we do not even have to apply energ... | g15904 | [
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<p>I have a cylinder filled with water in it at the bottom of the ocean. Say 100 meters down. In this cylinder is a piston that moves up and down. Its job is to squish the water out the bottom of the cylinder to create an air space in the top half of the cylinder. There are lots of holes to let the water move freely ou... | g15905 | [
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<p>According to Sommerfeld the derivative of the density of states $g'(\varepsilon)$ apears in several thermodynamic quantities. Will this also be the case if one use the correct dispersion relation of crystal? If yes don't we encounter the divergence in these quantities when we pass a van Hove singularity (where $g'(\... | g15906 | [
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0.02176111750304699,
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<p>Supernovae of type "Ia" are those without helium present, but with evidence of silicon present in the spectrum. The most accepted theory is that this type of supernova is the result of mass accretion on a carbon-oxygen white dwarf from a companion star, usually a red giant. This can happen in very close binary star ... | g15907 | [
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<p>From an interesting <a href="http://www.sciencedaily.com/releases/2011/09/110915083715.htm" rel="nofollow">ScienceDaily</a> article, I read this</p>
<blockquote>
<p>Before the groups of stars disperse, binary stars move through their
birth sites and the group studied how they interact with other stars
gravita... | g15908 | [
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0.02497466653585434,
0.... |
<p>I'm wondering whether the <strong>residual light of the <a href="http://en.wikipedia.org/wiki/Big_Bang" rel="nofollow">Big Bang</a></strong> comes from one particular <strong>direction</strong> and what possibilities do we have to detect its position?</p>
<p><img src="http://i.stack.imgur.com/VJboT.jpg" alt="Enter ... | g15909 | [
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-0.... |
<p><img src="http://i.stack.imgur.com/vxYJd.png" alt="enter image description here"></p>
<p>Can M3 move upwards and M2 move to the right? in the solutions they assume this, but I find it impossible, it doesn't make sense physically.
I get the answer wrong if I assume M3 moving down and M2 moving right in the next que... | g15910 | [
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<p>I read something explaining that g-waves actually repel space-time. It described the following. Mass bends space-time creating gravity. An object like the sun, if it suddenly disappeared the space-time it bent would spring back up and the space it compressed (it's gravity well) would form a gravity wave that woul... | g15911 | [
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<p>If I have a potential given by:
$$U=U_0\left[2\left(\frac xa\right)^2-\left(\frac xa\right)^4\right]$$
It says that at $t=0$, the particle is at the origin ($x=0$) and the velocity is positive and equal to the escape velocity, which I found to be $\sqrt {2U_0/m}$
I have the differential equation:
$$m\ddot x=-\nabla ... | g15912 | [
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0.01746... |
<p>We know that Dirac equation is</p>
<p>\begin{equation}
( i \partial _\mu \gamma ^\mu - m ) \psi ~=~0.
\end{equation}</p>
<p>How can we show that Dirac equation is invariant under CPT transformation?</p> | g15913 | [
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<p>I learned it during my environment class.
My professor introduced the concept--- ratio of surface area and volume.
The numerator has connections with the radiative loss, while the denominator is associated with the heat content.
The ratio is inversely proportional to the radius of the planet.
The conclusion is if I ... | g15914 | [
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0.006695774849504232,
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0.057075586169958115,... |
<p>I know that a force does no <a href="http://en.wikipedia.org/wiki/Work_%28physics%29" rel="nofollow">work</a> on an object if the object's displacement is zero, but if an object is moving at a constant velocity $\bar{v}$, and a force $\bar f$ (let's say that $\bar f$ and $\bar v$ have the same direction) acts upon i... | g15915 | [
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<p>I am facing this topic for the umpteenth time in my college career and, of course, every teacher has explained it in a different way.</p>
<p>In this course, to find the expression of the electric field of a uniformly charged sphere, the professor started from this equation.</p>
<p>$$
\frac{1}{r^2}\ \frac{\partial}... | g15916 | [
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0.03255235403776169,
-0.008270657621324062,
0.0481... |
<p>Consider a pure <a href="http://en.wikipedia.org/wiki/Yang_Mills" rel="nofollow">Yang-Mills</a> lagrangian density $$\mathcal{L}=-\frac{1}{4}F^{\mu\nu}_aF^a_{\mu\nu}$$ with gauge group $U(2)$.</p>
<p>Take the generators for $U(2)$ to be $t_0$, $t_i \ i=1,...,3$ with commutation relations given by
$$[t_0,t_i]=0$$
$... | g15917 | [
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0.048382267355918884,
0.007187787909060717,
0.023246... |
<p>It seems to me that the popular suggestive explanation of dark flow is another universe interacting with ours. Isn't there other alternative explanations? </p> | g15918 | [
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0.0674992... |
<p>What is the point of having 45 degreed blade in Guillotine? After all, the pressure-Force over Area-blade imposes to the neck is the same either way. </p> | g662 | [
0.07597276568412781,
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... |
<p>If we have 2 batteries one of emf x and the other is of emf y and we connect them in series we get an effective emf of x+y.</p>
<p>But what if we connect them in parallel, how to calculate the emf now?</p> | g364 | [
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0.018... |
<p>According to recent measurements our observable universe is roughly 93 billion light years in diameter; also it appears (according to WMAP measurements) that spacetime is flat.</p>
<p>Supposing space is infinite.</p>
<p>It seems to me that it isn't outside logical possibility that there is another observable unive... | g15919 | [
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0.0550116... |
<p>Our ability to store data on or in physical media continues to grow, with the maximum amount a data you can store in a given volume increasing exponentially from year to year. Storage devices continue to get smaller and their capacity gets bigger. </p>
<p>This can't continue forever, though, I would imagine. "Thing... | g647 | [
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<p>This spawns from part of an answer to a question I asked. </p>
<blockquote>
<p>All sorts of things go to 0 and/or ∞ if you start boosting at c, and
so you cannot boost into and out of a photon's frame.</p>
</blockquote>
<p>It somewhat relates to a video from the discovery channel where they talk about space, t... | g15920 | [
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0.04079772159457207,
-0.011661580763757229,
0.013133196160197258,
0.042... |
<p>I'm using the standard equation for the <a href="http://en.wikipedia.org/wiki/Range_of_a_projectile" rel="nofollow">range of a projectile</a>:</p>
<p>\begin{align}
d &= \frac{v\ \text{cos}\theta}{g} \left( v\ \text{sin}\theta + \sqrt{v^2\ \text{sin}^2\theta + 2gy_0}\right)
\end{align}</p>
<p>where $d$ is the h... | g15921 | [
0.02830738201737404,
-0.042462967336177826,
-0.0020534840878099203,
-0.02779039926826954,
0.05294856056571007,
0.034895628690719604,
0.04370085150003433,
-0.0009309194865636528,
-0.05047963559627533,
0.03754951059818268,
-0.023206794634461403,
0.013276509009301662,
0.060086674988269806,
-0... |
<p>Let's say the Earth is an airless sphere. What speed would an object weighing 1 kg need to leave the surface at in order to get to and be motionless at L1, where the Moon's gravity becomes stronger than the Earth's gravity?</p> | g15922 | [
0.02411283366382122,
0.048240456730127335,
0.011079302988946438,
0.011939441785216331,
0.0011174057144671679,
0.0243533942848444,
0.015417995862662792,
-0.00290232733823359,
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-0.0030842763371765614,
0.007531887385994196,
-0.012942497618496418,
-0.026397110894322395,
0.0... |
<p>As an example of such a historical myth that we all learned, there is the story that in his confrontation with Cardinal Bellarmine in 1632, Galileo had all the evidence on his side, won the intellectual argument by the weight of that evidence, and was defeated only by the ignorant prejudices the trial judges. Howe... | g15923 | [
0.03886251151561737,
0.021832671016454697,
0.017373431473970413,
-0.023434679955244064,
-0.009395084343850613,
0.07003693282604218,
0.049422211945056915,
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0.03896625339984894,
-0.009525347501039505,
0.04228707775473595,
-0.016666462644934654,
0.061883844435214996,
-0.0... |
<p>I'm reading an article about two-dimensional infrared spectroscopy and I don't understand the following sentence.</p>
<blockquote>
<p>Bleach or stimulated emission contributions yield negative signals.</p>
</blockquote>
<p>What are "bleach contributions"? I have never heard of it and cannot find a suitable expla... | g15924 | [
0.024654466658830643,
-0.0005065417499281466,
0.018420075997710228,
-0.0005483768181875348,
0.050720348954200745,
0.0167335607111454,
0.02423153631389141,
0.04965286701917648,
-0.030768297612667084,
-0.04240358993411064,
-0.024990076199173927,
0.060276955366134644,
0.044242776930332184,
0.... |
<p>From the first law of thermodynamics:</p>
<p>$$ dU = TdS - PdV + \sum_i\mu_i dN_i.$$</p>
<p>Quoting <a href="http://en.wikipedia.org/wiki/Internal_energy#Internal_energy_of_multi-component_systems" rel="nofollow">Wikipedia</a>:</p>
<blockquote>
<p>As conjugate variables to the composition $N_{i}$ the chemical p... | g15925 | [
-0.0024334487970918417,
0.03015558235347271,
-0.02269510179758072,
-0.0393696129322052,
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0.041118379682302475,
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-0.006419629789888859,
-0.04208805412054062,
-0.014941422268748283,
0.009809497743844986,
... |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/49862/how-is-the-speed-of-light-constant-in-all-directions-for-all-observers">How is the speed of light constant in all directions for all observers?</a> </p>
</blockquote>
<p>Is the speed of light const... | g489 | [
0.024852240458130836,
0.002495398046448827,
0.008336992003023624,
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-0.014184591360390186,
0.03452194109559059,
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0.023506272584199905,
0.04626... |
<p>I am a bit confused by the concepts of <a href="http://en.wikipedia.org/wiki/Active_and_passive_transformation">active and passive transformations</a>. In all the courses I am doing at the moment we do transformations of the form:
$$
\phi(x) \rightarrow\phi'(x') = \phi(x)
$$
and
$$
\partial_{\mu}\phi(x)\rightarrow\p... | g15926 | [
0.005946443881839514,
-0.03418499231338501,
-0.02944159507751465,
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0.062017474323511124,
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0.005176874343305826,
-0.056123241782188416,
0.022226551547646523,
-0.0005710081895813346,
0.0... |
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