The commutator of x with the Hamiltonian H.[x, H] is

(d) -ih/m p x. Explanation: [x, H] = [x, p²/2m] = (1/2m)(2iħp) = iħ px/m.

Q93 · CSIR-NET Chemistry, June 2016

Paper: CSIR-NET June 2016 · Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Postulates Operators · Marks: 2 · Difficulty: Easy

The commutator of x with the Hamiltonian $\hat{\mathrm{H}} .[\hat{\mathrm{x}}, \hat{\mathrm{H}}]$ is

(a)0

(b)ih

(c)$-\frac{\mathrm{h}^{2}}{2 \mathrm{m}} \hat{\mathrm{p}} \mathrm{x}$

(d)$-\frac{\mathrm{ih}}{\mathrm{m}} \hat{\mathrm{p}} \mathrm{x}$

Answer

Answer: D ✓ checked by 4AB · confidence high

The source book printed no answer; this one was worked out and checked — see the explanation.

Explanation

[x, H] = [x, p²/2m] = (1/2m)(2iħp) = iħ p_x/m.

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