$$H = \frac{p^2}{2m} + \frac{1}{2} m \omega^2 x^2$$
(Please provide the actual problems you'd like help with, and I'll do my best to provide step-by-step solutions) zettili chapter 10 solutions
Here's what I found:
(a) Show that the Hamiltonian for a one-dimensional harmonic oscillator can be written in terms of the creation and annihilation operators. The Hamiltonian for a one-dimensional harmonic oscillator is given by: $$H = \frac{p^2}{2m} + \frac{1}{2} m \omega^2 x^2$$