Recent content by VoxCaelum

Well, for starters the second equation you wrote down doesn't make too much sense, since there is a sum over s on the right hand side, but there is still an s on the left hand side. Now the actual problem, you should convince yourself that when taking the commutator...

Thanks! So now imagine the case where I second quantize my system, and I'm talking about fermions, that is I have the anti-commutator $$ \left[a^{\dagger}_{i},a_{j}\right]_{-} = \delta_{ij}, $$ for the field creation operators in momentum space. And say I have some other operators say b and c...

When (canonically) quantizing a classical system we promote the Poisson brackets to (anti-)commutators. Now I was wondering how much of Poisson bracket structure is preserved. For example for a classical (continuous) system we have $$ \lbrace \phi(z), f(\Pi(y)) \rbrace = \frac{\delta...

I meant it would be the Fourier transform in the classical limit. And you're right about me getting that factor wrong. I misremembered there being a square root.

Thanks again. I believe the current prefactor \frac{1}{\sqrt{2 \pi}} is still correct, but it will be taken care of once you divide by 2 \pi \hbar and compute the last integral, which is the Fourier transform of |\psi|^{2}.

Thanks! I gave that a try, and this is what I came up with: \begin{equation} f(p,q) = \frac{\hbar}{2 \pi} \int_{ℝ^{2}} \int_{ℝ} \psi^{\star}(x-\hbar u) e^{ev(x-\hbar u)} \psi(x) e^{i \hbar u v/2 -ipu -iqv/} du dv dx \end{equation} Which I think should be combined as follows so I get an...

I am trying to solve the following problem on an old Quantum Mechanics exam as an exercise. Homework Statement Homework Equations I know that the trace of an operator is the integral of its kernel. \begin{equation} Tr[K(x,y)] = \int K(x,x) dx \end{equation} The Attempt at a...

In the second equation I forgot a power of \phi'. Also I did not forget to do one of the E.L. equations. Because we are constrained to the surface of a sphere I simply set r'=0 and treated r as a constant parameter instead of a dynamical variable. This reduces the Lagrangian (in spherical...

I don't think this should go in advanced physics... But if you want to play around with lissajous figures you could check this out: http://www.wolframalpha.com/input/?i=lissajous+figure You can change the number in the boxes to change the figures.

Homework Statement Consider a particle moving on a two dimensional sphere of radius r, whose Lagrangian is given by: L(q,q')=\frac{1}{2}m\sum(qi')2 (A) Transform the Lagrangian into spherical coordinates and write down the resulting Euler-Lagrange equations. (B) Solve the...

Currently I have no programming skills at all. I am considering mastering in Theoretical Physics and was wondering how strongly I would be recommended to learn some basic programming skills. Also if it is inconvenient to follow any programming classes at my university at the moment what would be...

Supposedly Hirsch and Smale have a really good book on this subject: https://www.amazon.com/dp/0123495504/?tag=pfamazon01-20 I'm not sure off the knowledge required to use this, but you could take a look using the Look Inside function. Good luck.

Popular science books won't really be usefull in preparing for college. I mean by all means read them if you think they're interesting but don't expect them to prepare you for what you're going to get in college. I would recommend something that actually goes into quantitative analysis of...

How is "Mechanics; a course of theoretical physics volume 1", by Landau and lifshitz? I have recently bought Volume 2 of this series (the classical theory of fields) because it was recommending for an undergrad course I'm following. I was wondering how good this first part was. I'm mainly...