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<p>Consider the operator $$T=pq^3+q^3p=-i\frac{d}{dq}q^3-iq^3\frac{d}{dq}$$</p> <p>defined to act on the Hilbert Space $H=L^2(\mathbb{R},dq)$ with the common dense domain $S(\mathbb{R})$. Here $S(\mathbb{R})$ denotes Schwartz space. </p> <p>How would I show that this operator is hermitian? </p> <p>I understand the p...
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<p>I have read from many sources that the Fraunhoffer diffraction pattern is the Fourier transform of the grating. But I feel like these explanations do not take into account the curvature of the initial beam. </p> <p>Let's say my grating is defined by $G(x)$. I have a beam $E(x)$ incident on the grating and want to k...
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<blockquote> <p><strong>Q:</strong> A $0.150\text{ kg}$ glider is moving to the right ($+x$) on a frictionless, horizontal air track with a speed of $0.80\text{ m/s}$. It has an elastic collision with a $0.300\text{ kg}$ glider moving to the left ($-x$) with a speed of $2.20\text{ m/s}$.</p> <p><strong>a.)</...
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<p>I'm trying to understand the way that Hamilton's equations have been written in <a href="http://pubs.rsc.org/en/content/articlelanding/2010/fd/b902479b" rel="nofollow">this paper</a>. It looks very similar to the usual vector/matrix form of Hamilton's equations, but there is a difference.</p> <p>$$\frac{{\bf dZ}(t)...
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<p>This image from wikipedia, explains that there occurs a potential drop across a <a href="http://en.wikipedia.org/wiki/P%E2%80%93n_junction" rel="nofollow">pn semiconductor junction</a>, and an electric field confined to the depletion region.<img src="http://i.stack.imgur.com/7VaN3.png" alt="enter image description h...
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<p>For example, let us examine the case of quantum (discrete) fourier transform.</p> <p>There are $2^N$ samples. How do we initialize these $2^N$ samples into $N$ qubits? I have a hard time understanding this. </p>
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<p>Based on the previous <a href="http://physics.stackexchange.com/questions/80294/is-the-su2-flux-defined-in-the-context-of-projective-symmetry-grouppsg-an">question</a> and the comment in it, imagine two different mean-field Hamiltonians $H=\sum(\psi_i^\dagger\chi_{ij}\psi_j+H.c.)$ and $H'=\sum(\psi_i^\dagger\chi_{ij...
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<p>I am stuck in this problem-</p> <p><img src="http://i.stack.imgur.com/CBC4d.png" alt="The Problem"></p> <p>I need to find the velocity of <a href="http://en.wikipedia.org/wiki/Efflux" rel="nofollow">efflux</a> at the hole of the container. [We can assume that the area of the hole is negligible in comparison with t...
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<p>I recently read R.P Feynman's <em>QED:A Strange Theory of Light and Matter.</em> It is believed that time travel to the past is not possible. Then why is particles going backward in time considered in the book while drawing Feynman diagrams?</p>
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<p>Let me start by apologizing if this question seems pedantic and say that I'm not very familiar with physics in general, as I'm a math major instead.</p> <p>Anyway, say a body changes from temperature $T_1$ to $T_2$, with $T_2 \ge T_1$.</p> <p>Then the change in temperature is $$\Delta T = T_2 - T_1$$</p> <p>Now, ...
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<p>I really don't understand with the linearity conditions I have where this comes from.</p>
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<p>What are <a href="http://www.google.com/search?q=Ramsey+interaction" rel="nofollow">Ramsey interactions</a>? I am researching atomic clocks and am not sure why the atoms need to be exposed twice to an electromagnetic field in order to cause excitation.</p>
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<p>Dose anyone has a clue what <a href="http://www.google.com/search?q=symmetric+fission" rel="nofollow">Symmetric Fission</a> is?</p> <p>I couldn't find any explanation on what is it on internet.</p>
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<p>Can <a href="http://en.wikipedia.org/wiki/Bose%E2%80%93Einstein_condensate" rel="nofollow">Bose-Einstein condensate</a> be written as non-linear wave equation (in terms of mean field approximation theory)? the equation is: <img src="http://i.stack.imgur.com/X8kEs.png" alt="enter image description here"></p> <p>sour...
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<p>I understand that an event, in a four dimensional space-time, produces a light cone. As time increases the cones gets larger on either side of the event (past and future). For example the if the sun where to "go out" it would take 8 minuets for the earth to be affected by it simply because it takes approximately 8 m...
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<p>This probably includes a little of biology, but I believe it's mainly physics, so I hope it's ok to ask here:</p> <p>Imagine 2 persons: Person A weights 120 pounds and person B weights 180 pounds.</p> <p>Imagine they both fall from a big height:<br> a) landing on their knees (a good jump)<br> b) falling on their b...
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<p>The formula used in Gyrochronology that relates a star's Period of Rotation-Mass-Age is empirical? </p> <p>This news <a href="http://kepler.nasa.gov/news/nasakeplernews/index.cfm?fuseaction=ShowNews&amp;NewsID=129" rel="nofollow">How to Learn a Star’s True Age</a> </p> <blockquote> <p>"“A star’s rotation slows ...
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<p>For the purpose of this question, let's restrict ourselves to BKL singularities. BKL cosmologies are homogeneous Bianchi type XIII and IV cosmologies which exhibit oscillatory chaotic behavior, although that's not relevant to this question. Most generic singularities can be approximated locally by a BKL solution. Th...
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<p>I remember once getting new Teflon (non-stick) cookware; however, when I tried this new cookware on my induction cooker the <em>cookware did not heat up</em>. My regular steel cookware worked just fine on the induction cooker, both before and after trying the Teflon cookware. I've heard from at least two other peo...
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<p>I'm sorry if this is somewhat a dumb question.</p> <p>First: "Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as <em>linear transformations of vector spaces</em>"</p> <p>I know little about particle physics, but to what I know, physicists o...
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<p>I'm using the SOFTSUSY package to generate the sparticle spectrum at the EW scale. One of the input parameters is the ratio of the up and down-type Higgs vevs commonly known as $\tan\beta$. The $\mu$ parameter is computed as an output by constraining the Z-boson mass to be compatible with experiment. I was wondering...
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<p>I was taught today that the Electromagnetic wave Theory is unable to explain black body radiation. The example that was given to me: When a metal is heated, it emits different frequencies of light as it gets hotter. If electromagnetic wave theory was correct, it would not be so, the frequency (color) of light would ...
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<p>From the <a href="https://en.wikipedia.org/wiki/Gross%E2%80%93Pitaevskii_equation" rel="nofollow">Gross-Pitaevskii equation</a> \begin{equation}i\hbar\frac{\partial\psi}{\partial t}=\left(-\frac{\hbar^2}{2m}\nabla^2+V+g|\psi|^2\right)\psi\end{equation} using the variational relation \begin{equation}i\hbar\frac{\part...
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<p>I've been looking deeply into many bibliographic references without finding the answer. I would be interested in knowing the numerical value of the critical 2d XY spin model on triangular lattice. Being derived analytically (if possible) or from Monte-Carlo doesn't matter.</p>
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<p><img src="http://i.stack.imgur.com/jKBIc.png" alt="enter image description here"></p> <p>I have trouble interpreting this illustration. I see why <strong>r</strong> (position) and <strong>a</strong> (acceleration) are the way they are, but what happened to <strong>v</strong>? Why is it smaller than its coordinates?...
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<p>I'll break this down to two related questions:</p> <p>With a fission bomb, Uranium or Plutonium atoms are split by a high energy neutron, thus releasing energy (and more neutrons). Where does the energy come from? Most books I've ever come across simply state e=mc2 and leave it at that. Is it that matter (say a pro...
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<p>What is the exact meaning of the word <a href="http://en.wikipedia.org/wiki/Vacuum">vacuum</a>? Is it just a state of very low pressure or is it nothingness (as in there is nothing)? Also, when we say space is vacuum - it must be referring to pressure as space has light travelling (which means photons) besides the b...
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<p>The following formula has been given in 't Hooft's black holes notes ($|\Omega \rangle$ is the vacuum state of Minkowski space, O is a operator):</p> <p>$$\langle \Omega| O|\Omega \rangle = \sum_{n \ge 0} \langle n | O | n \rangle e^{-2 \pi n \omega}(1-e^{-2 \pi \omega})=Tr(O \rho_{\Omega})$$</p> <p><strong>How do...
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<p>What is the difference and similarities between Stueckelberg mechanism and Higgs mechanism? They both make the gauge field massive. Is the Stueckelberg mechanism a special case about U(1) gauge fields of Higgs mechanism? Does there exist Spontaneously symmetry breaking in Stueckelberg mechanism?</p>
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<p>A giant set of bar bells floating in space (like two identical sized planets connected by a long rod) would have a centre of mass midway between the two on the connecting rod. But surely it would have two centres of gravity, one at each end? If you were standing on one of the "bells" or planets, and threw a rock i...
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<p>What would be the general form of Lagrange Equation when instead of a scalar field we have a vector potential? has anyone derived the klein gordon equation for a corresponding vector potential Lagrangian? </p>
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<p>I am quite confused by both these terms. I would like to know what's the exact difference between both these terms and which one is more accurate.</p>
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<p>What makes the two 'color-neutral' gluons $(r\bar r−b\bar b)/\sqrt2$ and $(r\bar r+b\bar b −2g\bar g )/\sqrt6$ different from the pure $r\bar r +b\bar b +g\bar g $ ?</p> <p>Why don't they result in long range (photon-like) interactions?</p>
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<p>Suppose you have a solid ball on a horizontal table.</p> <ol> <li>What is the direction of friction force when the ball I pushed horizontally and <strong>starts rolling</strong>?</li> <li>Why is the direction of friction as it is? </li> <li><p>Which forces acts at the contact point between delta time t0 to t1? (If ...
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<p>Given the equation $$F_{\text{net}} = ma$$</p> <p>Does this not imply that if the net force on a certain object is positive, its acceleration will also be positive, and theoretically this object would accelerate forever to an infinite velocity?</p> <p>i.e envision a block on a surface. If a person were to apply ...
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<p>Without any a priori knowledge of the mass, speed, distance, and size of local celestial bodies (aside from Earth's size), what can I calculate and how from my "backyard" through observation?</p> <h3>Edit:</h3> <p>My goal is to create a high-school level physics project that students can conduct over the course of...
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<p>The title sums it pretty much. Are all <a href="http://en.wikipedia.org/wiki/Diffeomorphism" rel="nofollow">diffeomorphism</a> transformations also <a href="http://en.wikipedia.org/wiki/Conformal_map" rel="nofollow">conformal transformations</a>?</p> <p>If the answer is that they are not, what are called the set of...
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<p>I am a math teacher and I have to teach a topic called "Bruchterme" and "Bruchgleichungen" in german (I don't know the english word for it). For example </p> <p>$$ \frac{x^2 - 3}{(x - 2)x^2} + \frac{4}{x} + 2 $$</p> <p>is a "Bruchterm" and </p> <p>$$ \frac{4x}{2x -3} = 4 - \frac{2x}{x-1} $$</p> <p>is a "Bruchgle...
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<p><strong>Explain me these projections please</strong></p> <p><strong>Context:</strong> I was reading a paper (<a href="http://pra.aps.org/abstract/PRA/v68/i5/e052307" rel="nofollow">Phys. Rev. A 68, 052307</a>) which involved <strong>mesoscopic coherent states of light</strong>. There, in order to calculate the unce...
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<p>If two rocks were tied together with a tight, absurdly long, non-elastic rope, and placed on planets at either end of Earth's observable universe - or beyond - What would happen?</p> <ol> <li>Is the structural integrity of the rope enough to "overcome" the expansion of the universe all along the rope, causing the r...
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<p>A car moves on a plane road in east-west direction.At what latitude of earth should it move so that induced EMF in the axle connecting it's wheels is maximum? A. At the poles B. At the equator C. At a latitude inclined at 45 degree to the equator</p>
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<p>Can someone tell me in layman's language how the $(1/2,1/2)$ represents a vector field and $(0,1/2)$ or $(1/2,0)$ represents spinors and $(0,0)$ represents scalar field. Please don't be pedantic on mathematics part. I didn't take a course on group theory yet. Give me physical arguments why this is true? I have come...
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<p>The coefficient of kinetic friction can be calculated using $\mu_k = F_k/F_n$. A change in angle does not affect the normal force, but doesn't a change in angle affect the friction? As in if the angle is steeper, wouldn't the object have a greater propensity to move down the slope, thus there will be less friction?<...
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<p>In cold weathers it is suggested to put a humidifier since the air gets too dry. I wonder how the humidity affects how much time is needed to get the air at a temperature of 20 Celsius degrees? I mean suppose you have a cold room and you want to heat the air, Will the process be slower or faster in relation to varia...
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<p>As the title says. It is common sense that sharp things cut, but how do they work at the atomical level? </p>
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<p>I'm looking to create a rain harvesting system. I have a 275 gallon IBC tote that is 48" x 40" x 46". I have an adapter for a 3/4 garden hose at the bottom of the IBC tote. I'm trying to figure out three things:</p> <ol> <li><p>What is the pressure at the bottom of the tote, assuming that the tote is full?</p></li>...
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<p>Why is it that the direction of an area vector should be always along the normal drawn to the surface? Can't it also be some other angles with the plane?</p>
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<p>Is dark matter a candidate to fill void left by <a href="http://en.wikipedia.org/wiki/Luminiferous_aether" rel="nofollow">luminiferous ether</a> as a medium for light travel?</p>
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<p>'In the answers to one of the questions based on rotation of a disc in my physics book the answer includes the statement 'As we know that the velocity of outermost point on a rotating disc is double the velocity of center of mass'. But, I didn't know that and why is it like that?</p> <p>My thinking: I know that as ...
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<p>What is the relationship between two eigenfunctions of the time-independent Schrödinger Equation (in one spatial dimension) if they both have the same eigenvalue?</p>
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<p>I read in a QFT book that local gauge symmetry implies causality. Could someone please explain that statement and why it's true?</p> <p>Thank you.</p>
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<p>I'm currently struggling with the expression of operators in second quantization. I did an exercise in which I had to consider a fermion in a central potential $V(\vec{r})$ and show that the matrix elements of $V(\vec{r})$ and $V_{ij} a_i a^{\dagger}_j$ were identical. I think I get this right. Yet, when I try to do...
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<p>In <a href="http://www.feynmanlectures.info/docroot/II_28.html#Ch28">Volume II Chapter 28</a> of the Feymann Lectures on Physics, Feynman discusses the infamous 4/3 problem of classical electromagnetism. Suppose you have a charged particle of radius $a$ and charge $q$ (uniformly distributed on the surface). If you...
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<p>I have a set of <a href="http://www.google.com/search?q=PLIF+images" rel="nofollow">PLIF images</a> of a passive scalar advected in a turbulent flow. I'm wondering if it's possible to estimate the integral length-scale based on the images of the passive scalar, and if so, how would I go about it. Any references to...
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<p>Almost every solid state physics textbook says crystal momentum is not really physical momentum. For example, phonons always carry crystal momentum but they do not cause a translation of the sample at all. </p> <p>However, I learned that in indirect-band-gap semiconductors, we need phonons to provide the crystal mo...
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<p>There's a conventional wisdom that the best way to minimize the force impact of a punch to the head is to lean into it, rather than away from it. </p> <p>Is it true? If so, why?</p> <p>EDIT: Hard to search for where I got this CW, but heres <a href="http://www.xomba.com/how_to_take_a_blow_to_the_head" rel="nofollo...
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<p>Does an analog of the Solovay-Kitaev theorem exist for quantum operations, a generalization of quantum gates that also includes all completely positive maps?</p>
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<p>I have a swimming pool of 5300Liters. I have a heating element from a washing machine taking 1min17s to heat a bucket (10L) of water from 22 degrees to 30 degrees celcius.</p> <p>the water in my pool is 19 degrees celcius.</p> <p>how long would it take to warm my pool to 30 degrees? How long would it take to warm ...
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<p>I have a box with $x,y,z$ all ranging from 0 to $l$. It has $V(x)$=0 inside and =$\infty$ outside. By extending the 1D Schrodinger equation, I have that the allowed energy eigenvalues are $\hbar^2\pi^2\over2ml^2$$(n_1^2+n_2^2+n_3^2)$. What is the degeneracy of the 1st excited energy level? By "1st excited energy lev...
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<p>I know that surface tension plays a key role in the formation of a bubble. I guess a bubble contains air inside it. Now how is it so that a soap bubble contains air both inside it and outside it?</p> <p>I will be grateful to an answer donor if he explains me the various stages of bubble formation. In brief "How ...
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<p>In class of Newton's laws of motion, it was explained that Newton's second law is valid only in inertial frames. Teacher give us a example by considering a lift which is going downwards with acceleration$=a$ then a man watching the lift from outside will write $mg-t=ma$ (where $m$ is mass of the lift and $t$ is upwa...
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<p>In the absence of nonconservative forces such as friction and air resistance, the total mechanical energy in a closed system is conserved. This is why that when I toss an object directly upwards, the kinetic energy $K = (1/2)mv^2$ is transformed into potential energy as it increases in height with potential energy $...
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<p>Regarding the future applications of terahertz technology, I thought we already knew the entire electromagnetic spectrum. In fact we do not, terahertz lies between microwaves and infrared radiation. The future applications of this is astonishing. For example, faster communications and next generation scanning and im...
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<p>There is a mass $m$ in a potential such that </p> <p>$$ V(r) = \left\{ \begin{array}{lr} 0, &amp; a \leq r \leq b\\ \infty, &amp; \text{everywhere else} \end{array} \right. $$ I am looking to find the solution $u(r)$ to the radial equation $$ -\frac{\hbar^2}{2m} u^{\prime \prime}(r) +...
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<p>How light years are measured. Once i remember the distance between earth and moon are measured by light which travels and comeback and by the delay the distance is calculated.. But how light years are calculated</p>
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<p>Consider this reverse biased diode : </p> <p><img src="http://i.stack.imgur.com/z9dZo.png" alt="enter image description here"></p> <p>I read that no or very small current flows in reverse biased diode as depletion layers get widened and huge resistance is offered so no electrons can cross it. But, why the electron...
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<p>I've heard occasional mentions of the term "bootstraps" in connection with the S Matrix. I believe it applies to an old approach that was tried in the 1960s, whereby - well I'm not sure - but it sounds like they tried to compute the S Matrix without the interaction picture/perturbation theory approach that we curre...
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<p>I am following Griffiths' Introduction to Quantum Mechanics, as well as an online lecture that follows a different book, and both sources give different equations for the general solution of the 1-D Schrodinger equation for a free particle. </p> <p>Griffiths has it as: $$\Psi(x,t)=\frac{1}{\sqrt {2\pi}}\int_{-\inft...
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<p>Can any one please let me know what is the general procedure to construct the momentum operator under some coordinate transformation? For example, I understand that if </p> <p>$${\bf{r}}\rightarrow{\bf{r'}}=a{\bf{r}}$$ </p> <p>then the momentum operator will change as: </p> <p>$$\frac{\partial}{\partial{\bf{r}}}\...
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<p>Consider a ideal conductor in free space.For all purposes here,the zero of the potential is taken at infinity.</p> <p>Suppose I give a charge $Q$ to the conductor.As a result,the conductor will have a potential $V$. The question is can we say that $$Q=CV$$ where $C$ is a constant which depends only on <strong>the s...
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<p>So, I was watching various sci channel shows, and they touch on how extremely massive stars live only 100k years, vs the sun which lives ~10 billion years, and dwarf stars live some unspecified time longer.</p> <p>So, lets say you have a galactic civilation, worried about "heat death", and in order to avoid it, the...
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<p>How can we see living cells underneath it?</p>
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<p>I realize the situation where a laser beam moves vertically in a moving vehicle<img src="http://i.stack.imgur.com/qoDgm.gif" alt="time dilation proof"></p> <p>but what if the laser beam was a normal ball If we do the same steps of the proof considering that the velocity of the ball is not absolute and will have dif...
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<p>In classical thermodynamics, <a href="http://en.wikipedia.org/wiki/Thermodynamic_equilibrium" rel="nofollow">equilibrium conditions</a> means maximum entropy for a closed state. However, people always talk about equilibrium for open systems as well. How can one say that an open system has reached equilibrium with ou...
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<p>I know that electric charge is lorentz invariant quantity and I can easily think of experiment to check that. Is a though experiment that can prove that also?</p>
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<p>Suppose my system involves:</p> <p>1) A mounted wheel with some outward flap</p> <p>2) A bullet already in motion</p> <p>Initially the net angular momentum is 0 and the net kinetic energy is just that of the speeding bullet.</p> <p>The bullet hits the flap, causing the wheel to turn, and continues on (slightly s...
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<p>When I close one eye and put the tip of my finger near my open eye, it seems as if the light from the background image bends around my finger slightly, warping the image near the edges of my blurry finger tip.</p> <p>What causes this? Is it the heat from my finger that bends the light? Or the minuscule gravity that...
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<p>The Hamiltonian of Bose-Hubbard model reads as $$H=-J\sum\limits_{&lt;i,j&gt;}b_i^{\dagger}b_j+h.c.+\frac{U}{2}\sum\limits_{i}n_i(n_i-1)-\mu\sum\limits_in_i~~~~~~~~~(1)$$ </p> <p>For this we plot phase diagram in ( $J/U$, $\mu/U$ ) space. </p> <p>Same way if I want to plot phase diagram of Hamiltonian which looks...
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<p>In <a href="http://en.wikipedia.org/wiki/Gordon_Kane" rel="nofollow">Gordon Kane</a>'s <a href="http://www.goodreads.com/book/show/15843083-supersymmetry-and-beyond" rel="nofollow"><em>Supersymmetry and Beyond</em></a> (p. 118), he states:</p> <blockquote> <p>String theory has to be formulated in nine space dimen...
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<p>A proton accelerated with electric field gives off E.M. radiation and therefore should lose mass. Larmor's formula gives us a value for the power emitted (varies as acceleration squared). However, as the proton picks up speed, it also gains mass. Now, say I set up an immense electric field which provides an immense...
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<p>As I checked, the energy-momentum tensor defined as ${T^\mu}_\nu=\frac{\partial {\cal L}}{\partial(\partial_\mu \phi)}\partial_\nu \phi-{\cal L}{\delta^\mu}_\nu$ at the solution $\phi$ of equation of motion(Euler-Lagrange equation) satisfies automatically the conservation law: $\partial_\mu{T^\mu}_\nu=0$, without an...
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<p>Yes the title is an odd question, so I will provide a little background! Recently the sheer amount of padlocks on the Pont d'Art in Paris caused a part of its railing to fall off. Similar padlocks have been found on the Eiffel tower, so naturally the first question that came to my head was: "How many padlocks would ...
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<p>So this has been really bugging me over the past few days (and forgive me if the answer is so simple). Let's say we're observing the Sombrero galaxy. </p> <p>It is about 29 million light years away and 50 thousand light yyears in diameter. So we should be observing the "front" of it at what it looked like 29 milli...
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<p>I am doing a scattering simulation of a gaussian wave packet on a finite square well. I have solved numerically the Schroedinger equation and I know the values of the wave function after the scattering process before and after the square well. To be more clear, this is the situation after the scattering process: (th...
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<p><em>This question related to <a href="http://physics.stackexchange.com/questions/51554/why-are-magnetic-lines-of-force-invisible">Why are magnetic lines of force invisible?</a> and is motivated by a comment of @BlackbodyBlacklight, based on that, the illustrating example may depend on that linked question as context...
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<p>Consider the following schematics of a Bainbridge mass spectrometer</p> <p><img src="http://i.stack.imgur.com/UDrwC.png" alt=""></p> <p><sub> (Source: <a href="http://www.schoolphysics.co.uk/age16-19/Atomic%20physics/Atomic%20structure%20and%20ions/text/Mass_spectrometer/images/1.png" rel="nofollow">http://www.sch...
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<p>This may sound dumb, but I have been observing that, If my mobile phone is placed on the wire of my hands free (earphones) and if my mobile vibrates, I could listen the vibration from the ear plugs. I first thought that it is just my imagination, but every time my mobile is placed on my earphones wire i could totall...
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<p>For example how radio signals of a base transceiver station (BTS) penetrate through buildings?</p>
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<p>Image we have an ultra-high intensity, ultra low frequency laser, with wattage on the order of terawatts and a wavelength on the order of a lightsecond. We rotate it that the electric field component is oriented on the $\hat z$ axis, then fire it at a macroscopic block with a positive electric charge. Because of the...
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<p>For example We know glass when rubbed by silk will become positively charged while the silk will be charged negative. </p> <p>What exactly makes glass appropriate for losing electrons in that experiment? (</p>
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<p>I was in a physics group, then a student (or a professor, I don't know) posted this-</p> <blockquote> <p>Mohammad Shafiq Khan > Physics > The space-time concept including the formula $E=mc^2$ are proved baseless in the published paper "Experimental &amp; Theoretical Evidences of Fallacy of Space-time Concept and ...
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<p>As I understand it, you can't see beyond the Cosmic Microwave Background Radiation because the plasma of the early universe was opaque to electromagnetic radiation. What if you had a "neutrino telescope" with sufficient resolution? Would you be able to observe the primordial universe from before recombination?</p>
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<p>It is a long time question for me. </p> <p>For me, it seems that WKB is applicable for a given $E$ if and only if $\hbar$ is sufficiently small. Or in other words, WKB is applicable if and only if the quantum number is large enough. </p> <p>Is this understanding right?</p> <p>I would take the exactness of WKB for...
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<p>It is very well-known that for bosonic operators a Gauge transformation can always be associated with it $$a\rightarrow e^{i\phi}a.$$ Obviously this is a Unitary transformation. Something like $$a^{\prime}=\mathcal{U}^{\dagger}a\mathcal{U}$$</p> <p>I want to know what is $\mathcal{U}$?</p>
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<p>Are there any exactly solvable models in statistical mechanics that are known to have critical exponents different from those in mean-field theory, apart from the two-dimensional Ising model? I wonder about this because most easily solved models are either mean-field or do not exhibit a phase transition (Ising chain...
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<p>I am reading at the moment the paper <a href="http://arxiv.org/abs/1401.5203" rel="nofollow">http://arxiv.org/abs/1401.5203</a> and try to reproduce the results. One result is the proximity correction $S_{\Sigma}$ to the system</p> <p>$$ e^{-S_{\Sigma}} =\frac{\int\prod_{j\sigma\omega}D\Psi_{j\sigma}\left(\omega\ri...
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<p>In my textbook, as a preliminary to Faraday's law of induction, magnetic flux is defined over a closed loop as </p> <p>$$\Phi_B = \oint \vec{B}\cdot d\vec{A}$$</p> <p>Then it draws a parallel with electric flux and says: "as in electric flux, $d\vec{A}$ is a vector of magnitude $dA$ that is perpendicular to a diff...
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<p>I know there are many examples of metals with a negative dielectric constant at optical frequencies. But what about insulators?</p>
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<p>I have a problem to understand what does exactly mean (definition, how is induced, in which direction works) "flaring stress" in reference to the thread relief of internally/externally threaded hydraulic accumulator body. I found that phrase in EN 14359 (very long and complicated formula) and in ASME VIII Div. 1 (it...
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<p>I am actually working with Green-Schwarz anomaly cancellation mechanism in which I have came across a strange formula which relates trace in the adjoint representation (Tr) to trace in fundamental representation (tr).For the special case of $SO(n)$, the relation is </p> <p>$Tr(e^{iF})= \frac{1}{2}(tre^{iF})^2-\frac...
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