Q75 · CSIR-NET Chemistry, June 2016

Paper: CSIR-NET June 2016 · Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Particle In A Box · Marks: 2 · Difficulty: Easy

Average value of momentum for the ground state of a particle in a 1-d box is zero because

(a)$[\mathrm{p}, \mathrm{H}]=0$

(b)$\mathrm{V}($ potential $)=0$

(c)H is Hermitian

(d)the state is bound and stationary

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

A bound stationary state has a real (up to a phase) wavefunction, and for such a function ⟨p⟩ = 0; p does not commute with H for the box.

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