Using the commutator product rule and

PHYSICS · Subjective · Fermi University Physics · Quantum Mechanics · The formalism of quantum mechanics · The formalism of quantum mechanics

Quantum Mechanics: From the Photon to the Hydrogen Atom, Ch Observables, commutators and the uncertainty relations

Problem

Using the commutator product rule and [x^,p^]=iℏ[\hat x,\hat p] = i\hbar, derive [p^,x^2][\hat p,\hat x^2], and use the result to confirm the claim made in this chapter that [p^,H^]=−iℏmω2x^[\hat p,\hat H] = -i\hbar m\omega^2\hat x for the harmonic oscillator H^=p^2/2m+12mω2x^2\hat H = \hat p^2/2m + \tfrac12m\omega^2\hat x^2.

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