The commutator, [x, p²_x] is equivalent to

Question

Question

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CSIR-UGC (NET) Chemical Science: Held on (16 Feb 2022)

Answer 1

Concept:

For linear and position momentum:

[x̂, p̂_x] = iℏ ....(1)

[p̂_x, x̂] = -iℏ ...(2)

[x̂ⁿ, p̂_x] = nx^n-1 [x, p̂_x] ....(3)

[p̂_xⁿ, x̂] = np_x^n-1[p̂_x, x̂] .....(4)

Explanation:

Given → [x, p_x²]

→ Now using equation (4) and (1),

[x, p_x²] = 2 \(p_x^{2-1}\) [x, p_x]

= 2 p_x iℏ

Conclusion:-

∴ option '2' is correct i.e. [x, px2] = 2iℏp_x