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...
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...
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"...
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...
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]...
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...
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'...