Consider the Hamiltonian for a 1-dimensional harmonic oscillator. According to the quantization condition, Eq. (5.13), pq - qp is a diagonal matrix. Show that this is a necessary condition by proving that the matrix \(\mathbf{d}=\mathbf{p q}-\mathbf{q p}\) must be diagonal. Use the Hamilton equations of motion, but do not use Eq. (5.13).

Equation 5.13

Transcribed Image Text:

h pq-qp= 1 (5.13) 2ri =-ihl,