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    Electrons distinguishable ?

    They are, as a matter of fact, indistinguishible. Of course their dynamical properties differ, but indistinguishible means you cannot a priori know which one has that particular property. That is to say, if you somehow know that one electron has spin up, and other has spoin down, the...
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    Grover's Algorithm: is it really a search algorithm

    I'm wondering how it really is useful. The input for the, say 2-qubit, quantum computer that is running Grover's algoritm is |\Psi \rangle = (|1 \rangle + |2 \rangle + |3 \rangle + |4 \rangle) / \sqrt{4} And let us say we're looking the 3rd element in the so-called database. Now, Grover...
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    Gas with interacting molecules (from goldstein)

    Homework Statement (from Goldstein, problem 3.12) Suppose that there are long-range interactions between atoms in a gas in the form of central forces derivable from potential U(r) = \frac{k}{r^m}, where r is the distance between any pair of atoms and m is a positive integer. Assume further...
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    Where do electrons go while making a quantum jump?

    Electron may be somewhere near the nucleus or in Hawaii. I'd also like to add that electron is, as far as we know, a structureless point particle. What is smeared out is the wave-function associated with it. When you go measure it, you'll find that it's a point particle. The abrupt "quantum...
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    Probabilistic interpretation of wave function

    The star means complex conjugate: replaces all is with -is. In your case, \psi^* = A^* sin(\pi x / L), but you can takeA to be real, making \psi = \psi^*.
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    A problem from Sakurai

    Homework Statement (Sakurai 1.27) [...] evaluate \langle \mathbf{p''} | F(r) | \mathbf{p'} \rangle Simplify your expression as far as you can. Note that r = \sqrt{x^2 + y^2 + z^2}, where x, y and z are operators. Homework Equations \langle \mathbf{x'} | \mathbf{p'} \rangle = \frac{1}{ {(2 \pi...
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    Equation for S from state func and C

    Solved it.That equation I wrote will have an integration factor f(V). Using \frac{\partial S}{\partial V}_T = \frac{\partial P}{\partial T}_V, we have the solution for S, this time with an integration factor of T. By compraison of these two statements of S, it's perfectly defined.
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    Equation for S from state func and C

    Heat capacity of a liquid is C=T^4 and the state function is V(T,P) = Aexp(aT-bP) Derive an equation for entropy. Use the relevant Maxwell relations. dU = T dS - PdV \frac{\partial U}{\partial T}_V = C = T^4 \Rightarrow U = \frac{T^5}{5} + f(V) Since it's a liquid, and there're no...
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    Transmission amplitude using path-integrals

    Hello, As a path-integral newbie, I've been trying to calculate the amplitude for an electron which enters a box (potential within the box is given) at a point to emerge the other edge of the box (it doesn't matter when it exits). For simplicity, I first tried to work out the problem in one...
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    Intiutive approach to Green's function for SE

    Griffiths develops an intelgral equation for Scrödinger equation in his QM book. As doing so, he requires Green's function for Helmholtz equation (k^2 + \nabla^2) G( \mathbf r) = \delta^3(\mathbf r) A rigourious series of steps, including Fourier transforms and residue integrals follow...
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    Free Particle Action

    I've recently started Feynman & Gibbs. I was sure exercises will be fun, but i can't enjoy myself when i fail solving the first one! Exercise 1-1 says: show that free particle action is \frac{m}{2} \frac{x_b^2 - x_a^2}{t_b-t_a} I tried finding anti-derivative of \dot x^2, ended up with...
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    Induced E by a solenoid with time-varying current

    Cylindrical solution gave a better insight though. Since the system is symmetric around z-axis, the electric field should be independent of \theta, therefore, the solution is \mathbf E = -k \left(\frac{s}{2} \mathbf e_\theta \right). Wish that I had a more rigorous way to show it, though.
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    Induced E by a solenoid with time-varying current

    Thanks for the replies! Meir Achuz, I'd ask "why?" In cylindirical coordinates, z-component of curl is \frac{1}{s} \left( \frac{\partial (s A_{\theta}) }{\partial s} -\frac{\partial A_s}{\partial \theta} \right) = -k which has again 3 mathematically possible solutions -k/2(\frac{s}{2}...
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    Induced E by a solenoid with time-varying current

    Imagine a solenoid with n turns per length. Now, for an instant, in which everything looks static, the magnetic field inside the solenoid will be n \mu_0 I \mathbf e_z (choosing solenoid alinged with z-axis), and zero field outside. Now, what would happen if we change the current in time? To...
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    Point particle Lagrangian paradox!

    Thanks for the replies! I think i've developed a clear answer to the "paradox": The point particle configuration assumes no friction, the object freely slides under the gravity. However, in the rolling ball configuration, the is a friction, and it's responsible for the torque which causes...
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    Point particle Lagrangian paradox!

    Fixed the post. There is only one potential: V, and it is a potential which depends only the position of the object.
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    Point particle Lagrangian paradox!

    Suppose, there's an inclined surface, and a sphere, with radius R, is rolling without slipping. The Lagrangian is L = I \frac{\dot \theta ^2}{2} + m \frac{\dot s ^2}{2} - V where \theta is the angle of rotation of sphere and s is the curve length from top, and V is a potential which depends on...
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    Degeneracy of the 3d harmonic oscillator

    n is the sum of 3 quantum numbers, n_x, n_y, n_z; for the lowest rung, which is n=0, there's no degeneracy. For n=1, there's 3 fold degeneracy (one of the quantum numbers is 1, and rest is 0). For n=2, there's 6 fold degenertacy (one of them may be 2 and rest 0, or two of them may be 1) and so...
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    Relativistic invariance

    In Feynman lectures in physics v2 28-6, Feynman points out that we can add a constant times \phi to D'Alembertian without distrupting the relativistic invariance. How and why?? Can someone work out a mathematical proof? Thanks in advance.
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    Zero divergence in an enclosed point charge

    Actually, you don't get zero. Since the field depend only on radial distance, divergence is \mathbf \nabla \cdot \mathbf E = \frac{1}{r^2} \frac{\partial (r^2 \mathbf E)}{\partial r} which should be handled carefully at r=0, because of the denominator. Using divergence theorem, it can be shown...
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    How Many People Actually Understand QM?

    This reminds me another" [Broken]:
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    Laplace equation for parallel plate condersers

    This can't be true because plates are not infinite, and field lines are no longer straight lines when we approach to the edges: And how do we say potential itself does not depend on x either z? Apparently they do --even...
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    Laplace equation for parallel plate condersers

    I've recently started studying Laplace's equation and it's solution under various simple circumstances in electrostatics. I tried to solve the equation for a parallel plate condenser system, but I couldn't meet the boundary conditions. I had two plates, one placed on xz plane at y=0 (with...
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    Electrostatic pressure

    I have a metal sphere with the net charge q. And i'm trying to calculate the force that southern hemisphere exerts to northern hemisphere... and I get 0. now, the electrostatic "pressure" is \mathbf f = \sigma \mathbf E = (q/4\pi R^2) (q/4\pi \epsilon_0 r^2) \mathbf {e_r} due to the symmetry...
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    Degenerate perturbation theory question

    Eh ^-^' I mean, it doesn't tell anything about \alpha I was trying to ask how I would get \alpha and \beta. And secondly, how to solve the question (all seem "obvious", but how do I show them explicitly?). Maybe I should add that I'm a complete newbie to the subject (perturbation)!
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    Degenerate perturbation theory question

    This's a question from Griffiths, about degenerate pertrubation theory: For \alpha=0, \beta=1 for instance, eq. 6.23 doesn't tell anything at all! What does it mean "determined up to normalization"?. Equations 6.21 and 6.23 involve 3 unknowns (\alpha, \beta, E^1), and Griffiths solved them...
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    Expectation values

    How much sense does it make to compute expectation value of an observable in a limited interval? i.e. \int_a^b \psi^* \hat Q \psi dx. rather than \int_{-\infty}^{\infty} \psi \hat Q \psi dx Apparently, it shouldn't make any sense for it gives weird results when you compute e.v. of momentum for...
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    DS/dt = -H?

    Thanks vanesch, that leaves yo show \frac{\partial S}{\partial q} = p, but it appears to be as troublesome as the first question... (I'm a newbie to such things) I'll give it a try in the evening. This's simply a flame and I wonder where the admins are. Daniel, thank you for your warm...
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    DS/dt = -H?

    I'm trying to understand how \frac{\partial S}{\partial t} = -\mathcal{H}. I put the simplest/one dimensional Lagrangian (mv^2/2-V) and tried to derive it, but I failed: \frac{\partial S}{\partial t} = \frac{\partial }{\partial t} \int_{t_i}^{t_f} Ldt noting that x and \dot{x} is a function of...
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    Basic questions about QM computations

    1. How can we calculate expectation values of an arbitrary Q, even if \psi is not an eigenfunction of Q? 2. (Fourier transform related) Suppose I have piecewise wavefunction. \psi_{I} at (-\infty,-L), \psi_{II} at (-L,+L) and \psi_{III} at (L,+\infty). I can compute entire \phi(k) by taking the...