Recent content by Shadowz

Homework Statement Derive a microscopic version of the continuity equation given \rho(\vec{r},t) = \sum_{i=1}^N \delta(\vec{r}-\vec{q}_i(t)) and \rho is dynamic variablesHomework Equations I wonder if someone can point out the difference (in general) between the macroscopic and microscopic...

Ya right. Thank you. The rest is easy, I think.

Thanks, I got it. So we won't need r^2dr in the integral. I get the result that has sinh in it.

Hi, Thank for your help. I agree. So I tried \int_0^{2\pi}\int_0^{\pi} e^{-\beta \mu \epsilon \cos\Phi}sin\Theta d\Theta d\Phi but still gets the Bessel function. Is my limit of integration wrong? Should it be \int_0^{2\pi}\int_0^{\pi}\int_0^\infty e^{-\beta \mu \epsilon \cos\Phi} r^2...

Hi, So my attempt was to compute q = \int_0^{2\pi} e^{-\beta U} d\Theta But this gives me the Bessel function, so I am not sure if I am on the right track.

Homework Statement Given the perfect gas molecules with permanent electrical dipole moment u in the field \epsilon. The potential energy is U = -u\epsilon\cos\Theta Derive the additional effect of \epsilon on the heat capacity. I need some hints, please help. Thanks.

Homework Statement I am working a problem similar to this problem, (problem 2.18)...

Homework Statement So the question is I have to use some trial function of the form \sum c_if_i to approximate the energy of hydrogen atom where f_i=e^{-ar} for some number a (positive real number). Note that r is in atomic unit. Homework Equations Because r is in atomic unit, I think I should...

Can anyone please explain why S=- \ln\sum_{i=1}^N P_i^n for some integer n (for microcanonical ensemble). Thanks.

So all I try to do was to show that the coherent state has minimum uncertainty equally distributed between x and p. And the hint given was to show that \Delta x |\alpha> = x\Delta p |\alpha>, and thus it makes me think that I should treat \Delta x and \Delta p as operators rather than numbers.

Oh my question was how can you come up with such transformation; that is finding a U that satisfies U\sigma^3U^{-1}=\sigma_1 instead of a U that satisfies U\sigma^3=\sigma_1 Thanks,

Hi, How can I write \Delta x and \Delta p as operators? I want to show that \Delta x|\alpha> = c\Delta p|\alpha> where |\alpha> is coherent state. I feel like I have to write x and p in terms of annihilation operators, but I always think that \Delta x and \Delta p are numbers, not operators...

Thank you, Ya I am out of my misery. A tiny bit of problem was you wrote [a, a^\dagger]=\hbar which should be 1. But generally I get what you are talking about. Thanks.

Yes I think I get that from the previous post. So the coherent state |\alpha> = ce^{\alpha a^\dagger} |0> . Now I want to show that the normalized constant c is e^{-\frac{\alpha^2}{2}} So I do the dot product <\alpha|\alpha> = c^2 e^{a \bar{\alpha}}e^{\alpha a^\dagger} We consider e^{a...

Thank you for helping. I was careless when typing my last post. I read through wiki about BCH but only the last part of the page mentioned about annihilation operators, but then the explanation is not quite clear. So in short, is there a formula to find <\alpha| if knowing that |\alpha> =...