A particle moves in one dimension in the potential V=\frac{1}{2}k(t){x}^{2}, where k(t) is a time dependent parameter. Then \frac{d}{dt}\langle V\rangle. the rate of change of the expectation value \langle V\rangle of the potential energy, is

Basic Quantum Mechanics — CSIR Net PYQ (Question 3)

A Basic Quantum Mechanics previous-year question (PYQ) from Quantum Mechanics (CSIR Net). Read the question, check the correct answer, then practise the full topic.

Question 3 of 36 · 3.5 marks

A particle moves in one dimension in the potential

V = \frac{1}{2} k (t) x^{2}

, where

k (t)

is a time dependent parameter. Then

\frac{d}{d t} ⟨ V ⟩

. the rate of change of the expectation value

⟨ V ⟩

of the potential energy, is

1 $\frac{1}{2} \frac{d k}{d t} ⟨ x^{2} ⟩ + \frac{k}{2 m} ⟨ x p + p x ⟩$
2 $\frac{1}{2} \frac{d k}{d t} ⟨ x^{2} ⟩ + \frac{1}{2 m} ⟨ p^{2} ⟩$
3 $\frac{k}{2 m} ⟨ x p + p x ⟩$
4 $\frac{1}{2} \frac{d k}{d t} ⟨ x^{2} ⟩$

Correct answer: Option 1

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This Basic Quantum Mechanics PYQ is part of the Quantum Mechanics section of CSIR Net. Browse more Basic Quantum Mechanics questions or join the PhysicsByAaryan live batch for full conceptual coverage.