- #1
eep
- 227
- 0
Hi,
I'm trying to prove that for a particle in a potential V(r), the rate of change of the expectation value of the orbital angular momentum L is equal to the expectation value of the torque:
[tex]
\frac{d}{dt}<L> = <N>
[/tex]
where
[tex] N = r \times (-\bigtriangledown{V}) [/tex]
Basically, I'm having problems calculating the commutor of the Hamiltonian and the angular momentum operator, as
[tex]
\frac{d}{dt}<L> = \frac{i}{\hbar}<[H,L]> + <\frac{\partial{L}}{\partial{t}}>
[/tex]
Any hints on how I can calculate this?
I'm trying to prove that for a particle in a potential V(r), the rate of change of the expectation value of the orbital angular momentum L is equal to the expectation value of the torque:
[tex]
\frac{d}{dt}<L> = <N>
[/tex]
where
[tex] N = r \times (-\bigtriangledown{V}) [/tex]
Basically, I'm having problems calculating the commutor of the Hamiltonian and the angular momentum operator, as
[tex]
\frac{d}{dt}<L> = \frac{i}{\hbar}<[H,L]> + <\frac{\partial{L}}{\partial{t}}>
[/tex]
Any hints on how I can calculate this?