Recent content by phos19

I ran across the following problem : Statement: Consider a gas of ## N ## fermions and suppose that each energy level ## \varepsilon_n## has a multiplicity of ## g_n = (n+1)^2 ##. What is the Fermi energy and the average energy of this gas when ## N \rightarrow \infty## ? My attempt: The...

I've tried writing the curl A (in spherical coord.) and equating the components, but I end up with something that is beyond me: \begin{equation} {\displaystyle {\begin{aligned}{B_r = \dfrac{1}{4 \pi} \dfrac{-3}{r^4} ( 3\cos^2{\theta} - 1) =\frac {1}{r\sin \theta }}\left({\frac {\partial...

Since there is no friction : $$ m \ddot{x} = 0 $$ (no x motion).For the kinetic energy , I've tried: $$ K = 1/2 I_{cm} \dot{\alpha}^2 + 1/2 m v^2_cm = 1/2 I_{cm} \dot{\alpha}^2 + 1/2 m \dot{z}^2$$ . Giving me a weird expression , shouldn't the kinetic energy just be half the the moment...

yes ##H## is supposed to be squared. Here ##\vec{L}## is the canonical angular momentum, not the "naive" angular momentum.

yes, my mistake

Specifically given a purely magnetic hamiltonian with some associated vector potential : $$ H = \dfrac{1}{2m} (\vec{p} - q\vec{A}) $$ How can I deduce if $$ \vec{L} = \vec{r} \times \vec{p}$$ is conserved? ( $$\vec{p} = \dfrac{\partial L}{\partial x'}$$, i.e. the momentum is canonical)