The operator a (defind bellow) when operating on a harmonic energy eigenstate y, with energy En...

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The operator a (defind bellow) when operating on a harmonic energy eigenstate y, with energy En produces another energy eigenstate whose energy is En-hoo. Which of the following is true? P x+i- mo a = ma 2ħ I. a commutes with the Hamiltonian. II. a is a Hermitian operator and therefore an observable. III. The adjoint operator a #a (a) I only (b) II only (c) III only (d) I and II only The operator a (defind bellow) when operating on a harmonic energy eigenstate y, with energy En produces another energy eigenstate whose energy is En-hoo. Which of the following is true? P x+i- mo a = ma 2ħ I. a commutes with the Hamiltonian. II. a is a Hermitian operator and therefore an observable. III. The adjoint operator a #a (a) I only (b) II only (c) III only (d) I and II only

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