Hmmm, so this is valid for any operator, right? Now I got it. I did in this way before, but I thought that was wrong, because it wasn't working with the ##\vec{L}## operator. But I forgot an extra ##\epsilon_{ijk}## that appears in ##\left[L_{i},L_{j}\right]##. So this gives
$$ {\displaystyle...
Sorry, but I can't see how the Levi-Civita tensor cancels the anticommutator. I calculated the commutator using the position representation, as you mentioned. What I can't figure out is how I relate the commutator with the vector product ##\vec{\pi}\times\vec{\pi}##.
I have a question about this note: https://ocw.mit.edu/courses/physics/8-06-quantum-physics-iii-spring-2018/lecture-notes/MIT8_06S18ch2.pdf
I don't understand the expression (2.2.15). The complete relation would be
$$ \pi_i \pi_j = \frac{1}{2}\left(\left[\pi_i, \pi_j\right] + \left\{\pi_i...
Thank you very much! It's a really nice demonstration. The only thing I still didn't get it is the fraction of particles being ##\frac{A\cos\theta}{4\pi r^2}##. The ##cos(\theta)## term came from the flux of particles emerging from A? Also, why ##4\pi r^2## and not ##2\pi r^2## if the gas is in...
How can I find the relation between the radiance and the energy density of a black body? According to Planck's law, the energy density inside a blackbody cavity for modes with frequency ##\nu \in [\nu, \nu + \mathrm{d}\nu]## is given by $$ \rho(\nu, T)\mathrm{d}\nu =...