10 Solutions | Zettili Chapter

$$H = \frac{p^2}{2m} + \frac{1}{2} m \omega^2 x^2$$

We can express $x$ and $p$ in terms of the creation and annihilation operators: zettili chapter 10 solutions

(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: $$H = \frac{p^2}{2m} + \frac{1}{2} m \omega^2 x^2$$