Let the Hamiltonian H, in one-dimension, be H = (px²)/2m + V(x). The commutator of H with x, [H, x], is · ABC26PH0182

Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Postulates Operators · Exam: CSIR NET 2020 · Marks: 2 · Difficulty: Medium

Let the Hamiltonian H, in one-dimension, be

\[ H = \frac{p_x^{2}}{2m} + V(x). \]

The commutator of H with x, [H, x], is

(a)$\frac{-i\hbar}{m}\,p_x$

(b)$\frac{-i\hbar}{2m}\,p_x^{2}$

(c)$\frac{i\hbar}{m}\,p_x$

(d)$\frac{i\hbar}{2m}\,p_x$

Answer

Answer: A ✓ checked by 4AB · confidence high

Explanation

[H, x] = [p²/2m, x] = (1/2m)(p[p,x] + [p,x]p) = (1/2m)(−2iħp) = −iħp_x/m — option 1.

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