Recent content by damarkk

It's given a gas of particles all identical which has T fixed and spin S. Let's ##g(\epsilon)## the density of orbital states and ##g(\epsilon) = g_0## for ##\forall \epsilon \in [\epsilon_0, \epsilon_1]##, zero otherwise. How to compute the number of accessible quantum states of one...

You're right.

I'm sorry because this is very a stupid question :D (if you want delete it). Of course the mistake occurs because ##N(k)= \frac{V}{(2\pi)^3}\frac{4}{3}\pi k^3## and ##\frac{d N}{d k} = \frac{V}{(2\pi)^3}=4\pi k^2## I substitute ##k^2## with ##2m\epsilon/\hbar^2## and this is the error. The...

Suppose we have a gas of bosons with spin 0 and the grand potential is ##\Phi =\frac{kTV}{h^3} \int ln(1-e^{-\beta(p^2/2m -\mu})d^3p## we already integrated the function in the coordinate space and the result is the factor V (volume). Now, we know that ##\epsilon = p^2/2m## and ##d^3p = 4\pi...

Assume you have a microscopic pendulum you can suppose is like quantum harmonic oscillator. If the length of pendulum has variation of ##dl##, calculate the work on the pendulum and thermodynamic generalized force. Find also the variation of mean number of extitations. My Attempt Firstly, I...

I have one tremendous doubt about it. On ##t=0## the state of the oscillator is ##| \Psi (t) \rangle = | 1 \rangle ##. The perturbation is ##V(x)=\alpha x^3 = \alpha (\frac{\hbar}{2m\omega})^{3/2} (a+a^{\dagger})^3 = \gamma (a^3+3Na+3Na^{\dagger} + 3a + (a^{\dagger})^3)##. The only possible...

It doesn't matter obviously. But this is not my question. If you have hamiltonian like ##H = \hbar \omega N_x +\hbar \omega N_y## and if ##N_x |n_x n_y \rangle = n_x |n_x n_y \rangle##, ##N_y |n_x n_y \rangle = n_y |n_x n_y \rangle##, then ##H |n_x n_y \rangle = \hbar \omega (n_x + n_y) |n_x...

There is an hydrogen atom on a electric field along ##z## ##E_z= E_{0z}## . Consider only the states for ##n=2##. Solving the Saecular matrix for find the correction to first order for the energy and the correction to zero order for the states, we have: ##| \Psi_{211} \rangle##, ##|...

Thank you, sir. Sorry for this mistaken.

Hello to everyone. I'm sorry for the foolish question. The text is My attempt. = There are one fundamental state ## |0_x 0_y \rangle## with energy ##E_0=E_{0x}+E_{0y}=\frac{\hbar \omega}{2}+\frac{\hbar \omega}{2}=\hbar \omega ##. The first level has ##E_1 = 2\hbar \omega## and degeneration...

Some suggestions? Is my attempt correct? Thanks in advance.

Hello to everyone. I have some doubts about one problem of quantum mechanics. My attempt. I need to calculate the coefficient ##W_{ij}=<\psi_i | H' |\psi_j>## where ##H' = -eE(t)z## is a perturbation term in the hamiltonian and ##|\psi_i> = |\psi_{nlm}>##. We have four states and sixteen...

Hello to everyone. I'm an undergraduate physics student and a private teacher.