QuestionJune 6, 2025

When referring to the one-dimensional quantum harmonic oscillator, which of the following gives the commutator [hat (H),hat (a)^t] hwâ hwât 0 -hwâ

When referring to the one-dimensional quantum harmonic oscillator, which of the following gives the commutator [hat (H),hat (a)^t] hwâ hwât 0 -hwâ
When referring to the one-dimensional quantum harmonic oscillator, which of the following gives the
commutator [hat (H),hat (a)^t]
hwâ
hwât
0
-hwâ

Solution
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Answer

\hbar \omega \hat{a}^{\dagger} Explanation 1. Identify Operators \hat{H} is the Hamiltonian, \hat{a}^{t} is the creation operator. 2. Use Commutator Property For a quantum harmonic oscillator, [\hat{H}, \hat{a}^{\dagger}] = \hbar \omega \hat{a}^{\dagger}.

Explanation

1. Identify Operators<br /> $\hat{H}$ is the Hamiltonian, $\hat{a}^{t}$ is the creation operator.<br />2. Use Commutator Property<br /> For a quantum harmonic oscillator, $[\hat{H}, \hat{a}^{\dagger}] = \hbar \omega \hat{a}^{\dagger}$.
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