The wavefunction of a particle in onedimension is denoted by \psi (x) in the coordinate representation and by \phi (p)=\int \psi (x){e}^{- ipx/h}dx in the momentum representation. If the action of an operator \hat{T} on \psi (x) is given by \hat{T}\psi (x)=\psi (x+a), where a is a constant, then \hat{T}\phi (p) is given by

Basic Quantum Mechanics — CSIR Net PYQ (Question 2)

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 2 of 36 · 3.5 marks

The wavefunction of a particle in onedimension is denoted by

ψ (x)

in the coordinate representation and by

ϕ (p) = \int ψ (x) e^{- i p x / h} d x

in the momentum representation. If the action of an operator

\hat{T}

ψ (x)

is given by

\hat{T} ψ (x) = ψ (x + a

), where

a

is a constant, then

\hat{T} ϕ (p)

is given by

1 $- \frac{i}{h} a pϕ (p)$
2 $e^{- ia p /ℏ} ϕ (p)$
3 $e^{+ ia p / h} ϕ (p)$
4 $(1 + \frac{i}{h} a p) ϕ (p)$

Correct answer: Option 3

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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.