# Operator Bonanza

Suppose $$\hat { H } { \hat { a } }_{ + }{ \psi }_{ n } = ({E}_{n}+h\omega) { \hat { a } }_{ + }{ \psi }_{ n }$$, where $$\hat{H} {\psi}_{n} = {E}_{n} {\psi}_{n}$$ and $$\hat{H}$$ is a Hamiltonian operator for energy. Also, $${\psi}_{n}$$ is a completely valid quantum state.

What can one say about $${\hat{a}}_{+}{\psi}_{n}$$?

×