Recent content by kd6ac

Thank you for the link to partial derivatives. After reading it I realize that I might be wrong to think that ##p=f(x,p,t)##. I think it will help if I show you what I am trying to do and for that reason allow me to talk about an equivalent case in classical mechanics. Newtonian mechanics...

Dear andrewkirk, thank you so much for looking into this. I feel I should add a bit more background to the problem: Wigner's representation of quantum mechanics combines Schr\"odinger's position and momentum representations. The respective continuity equation takes the form, \begin{equation}...

In quantum mechanics, the velocity field which governs phase space, takes the form \begin{equation} \boldsymbol{\mathcal{w}}=\begin{pmatrix}\partial_tx\\\partial_tp\end{pmatrix} =\frac{1}{W}\begin{pmatrix}J_x\\J_p\end{pmatrix}...

Fourier transform of density matrix of cos(x+y)*cos(x-y) I would like to know whether there exists a solution to the following integral, \frac{1}{\pi} \int\limits_{-\infty}^{\infty} \cos(x+y)^\alpha \cos(x-y)^\alpha e^{2ipy} The above expression is the Fourier transform of the...

The Laguerre polynomials, L_n^{(\alpha)} = \frac{x^{-\alpha}e^x}{n!}\frac{d^n}{dx^n}\left(e^{-x}x^{n+\alpha} \right) have n real, strictly positive roots in the interval \left( 0, n+\alpha+(n-1)\sqrt{n+\alpha} \right] I am interested in a closed form expression of these roots...

It turns out that the equation you just showed me is a more general equation, so if k=n then the equation reduces down to the one I posted, and that is exactly what I wanted, thanks again

Thanks a lot, yes you are quite right, one should check the result and even derive it themselves. Wigner's function has certain properties which should always fulfil and if that is not enough you can derive the result for a few orthogonal states and then do the same with the formula you just...

I am new to physics forums and my frist post was actually this one but then I read somewhere that questions including your own study questions should go under homework, and therefore I posted it again under homework. The answer is not so important to have as I can ask any mathematical package...

The Wigner function, W(x,p)\equiv\frac{1}{\pi\hbar}\int_{-\infty}^{\infty} \psi^*(x+y)\psi(x-y)e^{2ipy/\hbar}\, dy\; , of the quantum harmonic oscillator eigenstates is given by, W(x,p) = \frac{1}{\pi\hbar}\exp(-2\epsilon)(-1)^nL_n(4\epsilon)\; , where \epsilon =...