Homework Statement
For a gas of N fermions of mass m confined in a volume V at a temperature ##T<E_F/kB##, consider the quantity ##<n_p>/V## as you would a classical distribution f(p,q) in the system phase space. Show that the impulse transfer of the elastic collisions of the particles with the...
Thanks, I'll do that, but I think the trick here was evaluating the consequences of the infinite potential. With positive x it just becomes an harmonic oscillator and I think simple conservation of energy implies the equipartition theorem. I didn't already do the calculations because my...
Homework Statement
For a gas of N fermions with mass M in 2D in a region of area A in thermal equilibrium at temperature T, we are asked to find ##U/N## in fuction of ##T## and ##a=A/N##.
The attempt at a solution
I used ##U=\sum(<n_i>\epsilon_i) = \sum(\exp(\beta(\mu-\epsilon_i))\epsilon_i...
I just have one question regarding the calculations. The integrals are defined for ##H<E## or we can also use ##E<H<E+\Delta##. In a region where a term of ##H## is infite, isn't the entire integral "broken" right off the bat?
I mean, unless there's something I'm missing, ##dH/dQ_i## comes out...
I'll give it a shot, the problem is that in my textbook they don't specify the Hamiltonian they use but I'll try doing the calculations myself. Do you mind giving me the final answer so I have something to compare my calculations to when I'm done?
Our syllabus follows Statistical Mechanics (Kerson, Huang) so that's the demonstration we used. As for the mathematical concepts used, integrals and averages I guess?
For the sake of brevity here's a printscreen of the last part of the demonstration.
The Hamiltonian we are given is of the...
So I have this question that goes like this, for a classical 1D system we are given an Hamiltonian of the form of an Harmonic Oscilator. However the term for the potential is infite when ##x\leq0## and the usual harmonical oscillator potential otherwise. The question is: is the equipartition...
Oh I see, I found it weird because I have an example from class that makes uses it the way I said, but in the case we only had two possible n-states 0 and 1 instead of a generic integer n, I suposse that's what makes the difference.
Okay, I redid the calculations and this pretty much breaks all...
I knew there was a reason I didn't include the |n+2> term in the first place. However what exactly is wrong about that other result?
It follows from applying ##\hat a |\psi_n>= \sqrt {n} |\psi_{n-1}>## to |n+1>
That would be ##\sqrt n |n>## but I think I did forget the terms for ##\hat a^\dagger|n+1>## and <n+1| which would be ##\sqrt{n+2}|n+2>## and the corresponding bra.
For a 1D QHO we are given have function for ##t=0## and we are asked for expectation and variance of P at some time t.
##|\psi>=(1/\sqrt 2)(|n>+|n+1>)## Where n is an integer
So my idea was to use Dirac operators ##\hat a## and ##\hat a^\dagger## and so I get the following solution
##<\hat...