The operator [x, [x, p²]] is identical with

Q89 · CSIR-NET Chemistry, June 2013

Paper: CSIR-NET June 2013 · Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Postulates Operators · Marks: 2 · Difficulty: Easy

The operator $\left[\hat{\mathrm{x}},\left[\hat{\mathrm{x}}, \hat{\mathrm{p}}^{2}\right]\right]$ is identical with

(a)$[\hat{\mathrm{p}} \hat{\mathrm{x}},[\hat{\mathrm{x}}, \hat{\mathrm{p}}]]$

(b)$[\hat{\mathrm{x}} \hat{\mathrm{p}},[\hat{\mathrm{x}}, \hat{\mathrm{p}}]]$

(c)$-\left[\hat{\mathrm{p}},\left[\hat{\mathrm{x}}^{2}, \hat{\mathrm{p}}\right]\right]$

(d)$-\left[\hat{\mathrm{x}},\left[\hat{\mathrm{x}}^{2}, \hat{\mathrm{p}}\right]\right]$

Answer

Answer: C ✓ checked by 4AB · confidence high

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

Explanation

[x, [x, p²]] = [x, 2iħp] = −2ħ². Also −[p, [x², p]] = −[p, 2iħx] = −2iħ(−iħ) = −2ħ². The others vanish (c).

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