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    Autocorrelation of a wiener process

    Let \phi(t) be a Brownian Walk (Wiener Process), where \phi\in[0,2\pi). As such we work with the variable z(t)=e^{i\phi(t)}. I would like to calculate E(z(t)z(t+\tau)) This is equal to E(e^{i\phi(t)+i\phi(t+\tau)}) and I know that E(e^{i\phi(t)})=e^{-\frac{1}{2}\sigma^{2}(t)}, where the...
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    Brownian motion solves Laplace's Equation?

    There seems to be a curious connection between Brownian Motion, stochastic diffusion process, and EM. I was hoping to share and to have someone add some insight on on what it means that the Dirichlet boundary...
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    LaTeX Custom Mathematica Shortcut: Copy as LateX

    This can be very useful, so I thought i'd share. If you edit the > Wolfram Research\Mathematica\8.0\SystemFiles\FrontEnd\TextResources\Windows\ file you can make Strl+Shift+C copy not plain but in LateX format. Very useful. Look for the line in the file that says "&LaTeX"...
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    Quantum Numbers of Spin 1/2

    this sounds like a question that should be answered somewhere, but i cant find it. how many quantum numbers does it take to specify the state of a spin 1/2? 1. if it points along z, then just 1: the eigenvalue of Sz will do (up to global phase) A. whether or not in a B field B. if...
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    Complex Conjugate: just replace i by -i even in denominator or inside argument?

    to get a Complex Conjugate of a #, is it ok to just replace i by -i even in denominator or inside argument?
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    Mathematica Mathematica: Fourier Transform by hand of sin

    Hi, i do not understand why i can find the FT of sin in mathematica using the built in function but not by integrating, even thoiugh they should be the same: Integrate[Exp[i(ω-ω0) t,{t, -∞, ∞}, Assumptions ->ω0 el Reals && ω el Reals] but the statment FourierTransform[Sin[ω0 x]...
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    SHO Ladder Method missed states?

    Following Griffiths derivation on pg 44 of the eigen-states of SHO Hamiltonian, he says that we can now find all eigenvalues, but doesnt say how he knows that a and a dagger will indeed take you between nearest neighboring orthogonal states. in other words, how do we know the ladder operators...
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    Photons in amorphous glass slow because?

    In solids it is the interaciton b/w the phonons and photons that give a lower effective speed. not absorption & re-emmision. (see ZapperZ's post: [Broken]) but in amorphous glass there are [B]no[B] phonons. So why does light 'slow down'...