- #1
Mark Spearman
- 3
- 0
Homework Statement
Calculate the quantized energy levels of a linear harmonic oscillator of angular frequency $\omega$ in the old quantum theory.
Homework Equations
\[
\oint p_i dq_i = n h
\]
The Attempt at a Solution
This is supposed to be a simple "exercise" (the first in Merzbacher). I believe the
answer is is $E_n = n \hbar \omega$. But I don't see how. The classical total energy of the LHO is
\[
H = m q_0^2 \omega^2/2
\]
so the energy would not be linear in omega. The solution using the Schroedinger equation is (n + 1/2) \hbar.
Thanks,
MLS