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1. 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...
2. Brownian motion solves Laplace's Equation?

There seems to be a curious connection between Brownian Motion, stochastic diffusion process, and EM. http://en.wikipedia.org/wiki/Stochastic_processes_and_boundary_value_problems I was hoping to share and to have someone add some insight on on what it means that the Dirichlet boundary...
3. 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\MenuSetup.tr 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"...
4. 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...
5. 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?
6. 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]...
7. 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...
8. 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: https://www.physicsforums.com/showthread.php?t=511177 [Broken]) but in amorphous glass there are [B]no[B] phonons. So why does light 'slow down'...