ADVANCED QUANTUM MECHANICS
PRACTICE EXAM QUESTION AND
CORRECT ANSWERS (VERIFIED
ANSWERS) PLUS RATIONALES 2026 Q&A
INSTANT DOWNLOAD PDF
1. Which operator generates spatial translations in quantum mechanics?
A. Hamiltonian
B. Angular momentum
C. Position operator
D. Momentum operator
Answer: D
Rationale: Momentum is the generator of spatial translations via the
unitary operator exp(−i a·p/ħ).
2. The commutator [𝑥 , 𝑝𝑥 ]equals:
A. 0
B. iħ
C. −iħ
D. ħ
Answer: B
Rationale: Canonical commutation relations define [x, p_x] = iħ.
3. A Hermitian operator guarantees:
A. Degenerate eigenvalues
B. Complex expectation values
C. Real eigenvalues
D. Nonlinear dynamics
, Answer: C
Rationale: Observables are represented by Hermitian operators with real
eigenvalues.
4. Which postulate links measurement outcomes to eigenvalues?
A. Superposition principle
B. Measurement postulate
C. Time evolution postulate
D. Correspondence principle
Answer: B
Rationale: Measurement postulate states outcomes are eigenvalues of the
observable operator.
5. The Schrödinger equation is:
A. Relativistic
B. Nonlinear
C. First order in time
D. Second order in time
Answer: C
Rationale: It is first order in time derivative, ensuring unitary time
evolution.
6. Time evolution in quantum mechanics is generated by:
A. Momentum
B. Hamiltonian
C. Position
D. Spin
Answer: B
Rationale: The Hamiltonian generates time translations.
7. The uncertainty principle arises from:
A. Measurement errors
B. Wave-particle duality
C. Non-commuting operators
D. Classical noise
, Answer: C
Rationale: Nonzero commutators impose intrinsic uncertainties.
8. A complete set of commuting observables (CSCO) is used to:
A. Define dynamics
B. Label unique quantum states
C. Break degeneracy
D. Measure probabilities
Answer: B
Rationale: A CSCO uniquely specifies quantum states.
9. Which operator corresponds to kinetic energy?
A. p²/2m
B. p/m
C. m v²
D. −ħ²∇
Answer: A
Rationale: Quantum kinetic energy operator is p²/2m.
10.The wavefunction normalization condition ensures:
A. Energy conservation
B. Momentum conservation
C. Total probability equals one
D. Orthogonality
Answer: C
Rationale: Probability interpretation requires total probability to be unity.
11.Degeneracy occurs when:
A. Eigenfunctions vanish
B. Multiple eigenstates share an eigenvalue
C. Operators do not commute
D. Energy is zero
Answer: B
Rationale: Degeneracy means different states correspond to the same
eigenvalue.
PRACTICE EXAM QUESTION AND
CORRECT ANSWERS (VERIFIED
ANSWERS) PLUS RATIONALES 2026 Q&A
INSTANT DOWNLOAD PDF
1. Which operator generates spatial translations in quantum mechanics?
A. Hamiltonian
B. Angular momentum
C. Position operator
D. Momentum operator
Answer: D
Rationale: Momentum is the generator of spatial translations via the
unitary operator exp(−i a·p/ħ).
2. The commutator [𝑥 , 𝑝𝑥 ]equals:
A. 0
B. iħ
C. −iħ
D. ħ
Answer: B
Rationale: Canonical commutation relations define [x, p_x] = iħ.
3. A Hermitian operator guarantees:
A. Degenerate eigenvalues
B. Complex expectation values
C. Real eigenvalues
D. Nonlinear dynamics
, Answer: C
Rationale: Observables are represented by Hermitian operators with real
eigenvalues.
4. Which postulate links measurement outcomes to eigenvalues?
A. Superposition principle
B. Measurement postulate
C. Time evolution postulate
D. Correspondence principle
Answer: B
Rationale: Measurement postulate states outcomes are eigenvalues of the
observable operator.
5. The Schrödinger equation is:
A. Relativistic
B. Nonlinear
C. First order in time
D. Second order in time
Answer: C
Rationale: It is first order in time derivative, ensuring unitary time
evolution.
6. Time evolution in quantum mechanics is generated by:
A. Momentum
B. Hamiltonian
C. Position
D. Spin
Answer: B
Rationale: The Hamiltonian generates time translations.
7. The uncertainty principle arises from:
A. Measurement errors
B. Wave-particle duality
C. Non-commuting operators
D. Classical noise
, Answer: C
Rationale: Nonzero commutators impose intrinsic uncertainties.
8. A complete set of commuting observables (CSCO) is used to:
A. Define dynamics
B. Label unique quantum states
C. Break degeneracy
D. Measure probabilities
Answer: B
Rationale: A CSCO uniquely specifies quantum states.
9. Which operator corresponds to kinetic energy?
A. p²/2m
B. p/m
C. m v²
D. −ħ²∇
Answer: A
Rationale: Quantum kinetic energy operator is p²/2m.
10.The wavefunction normalization condition ensures:
A. Energy conservation
B. Momentum conservation
C. Total probability equals one
D. Orthogonality
Answer: C
Rationale: Probability interpretation requires total probability to be unity.
11.Degeneracy occurs when:
A. Eigenfunctions vanish
B. Multiple eigenstates share an eigenvalue
C. Operators do not commute
D. Energy is zero
Answer: B
Rationale: Degeneracy means different states correspond to the same
eigenvalue.
