Riley hobson bence · Problem 19.7

Quantum operators

Mathematics — Methods · quantum-operators-harmonic-oscillator-ladder

Problem

For a quantum harmonic oscillator Hamiltonian involving operators

A

A^\dagger

, and the identity

I

, express the total Hamiltonian in terms of

B = A + gI

for some scalar

g

, and determine the value of

\left[B, B^\dagger\right]