13 Jun 2026

Quantum Mechanics Standard Problems

Standard competitive exam problems in quantum mechanics with answer key.

quantum-mechanics gate-2024 csir-net-2023 jest-2022

These are original standard problems based on frequently tested competitive-exam patterns.

Q: The canonical commutator of position and momentum is
A: $[x,p]=0$
B: $[x,p]=i\hbar$
C: $[x,p]=\hbar^2$
D: $[x,p]=ip^2$
ANSWER: B
SOURCE: GATE 2024 style
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Q: The ground-state energy of a one-dimensional infinite well of width $L$ is
A: $0$
B: $\pi^2\hbar^2/(2mL^2)$
C: $h^2/(mL^2)$
D: $\hbar\omega/2$
ANSWER: B
SOURCE: CSIR-NET 2023 style
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Q: For orbital angular momentum $l=1$, the allowed $m$ values are
A: $0,1$
B: $-1,0,1$
C: $-2,-1,0,1,2$
D: $1$ only
ANSWER: B
SOURCE: JEST 2022 style
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Q: The parity of the wavefunction $\psi(x)=x e^{-x^2}$ is
A: even
B: odd
C: neither even nor odd
D: periodic
ANSWER: B
SOURCE: GATE 2021 style
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Q: For a normalized wavefunction $\psi$, the probability density is
A: $\psi$
B: $|\psi|^2$
C: $\nabla\psi$
D: $\psi^2/2m$
ANSWER: B
SOURCE: CSIR-NET 2020 style
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Q: For a harmonic oscillator, the ground state energy is
A: $0$
B: $\hbar\omega/2$
C: $\hbar\omega$
D: $3\hbar\omega/2$
ANSWER: B
SOURCE: GATE style
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Q: If $[A,B]=0$, then $A$ and $B$ can have
A: no eigenstates
B: simultaneous eigenstates, when nondegenerate conditions allow
C: only imaginary eigenvalues
D: zero expectation values only
ANSWER: B
SOURCE: CSIR-NET style
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Q: The expectation value of momentum for a real bound-state wavefunction with definite parity is
A: necessarily nonzero
B: zero
C: infinite
D: equal to mass times position
ANSWER: B
SOURCE: JEST style

Problem Sheet Standard MCQs