QUANTUM MECHANICS QUALIFYING
EXAM QUESTION AND CORRECT
ANSWERS (VERIFIED ANSWERS) PLUS
RATIONALES 2026 Q&A INSTANT
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1. The time-dependent Schrödinger equation describes
A. Measurement outcomes
B. Classical trajectories
C. Time evolution of the wavefunction
D. Operator eigenvalues
Answer: C
Rationale: The Schrödinger equation governs how the quantum state evolves in
time.
2. The wavefunction ψ(x,t) represents
A. Charge density
B. Energy density
C. Probability amplitude
D. Particle trajectory
Answer: C
Rationale: The squared magnitude |ψ|² gives probability density.
3. An operator corresponding to momentum in position space is
A. x
B. ∂/∂x
, C. −iħ ∂/∂x
D. ħx
Answer: C
Rationale: Canonical quantization gives momentum as a derivative operator.
4. The expectation value of an observable A is
A. Eigenvalue of A
B. Maximum value of A
C. ⟨ψ|A|ψ⟩
D. Tr(A)
Answer: C
Rationale: Expectation values are inner products with the operator.
5. Operators A and B commute if
A. AB = 0
B. AB = BA
C. A = B
D. A† = B
Answer: B
Rationale: Commutation means the product is order-independent.
6. The uncertainty principle arises from
A. Measurement error
B. Classical noise
C. Non-commuting operators
D. Relativity
Answer: C
Rationale: Operator non-commutation leads to intrinsic uncertainties.
7. The ground state energy of a 1D harmonic oscillator is
A. 0
B. ħω
, C. ½ħω
D. 2ħω
Answer: C
Rationale: Zero-point energy is half a quantum.
8. Ladder operators are useful because they
A. Diagonalize position
B. Remove time dependence
C. Connect energy eigenstates
D. Eliminate uncertainty
Answer: C
Rationale: Creation and annihilation operators raise or lower energy levels.
9. A normalized wavefunction satisfies
A. ψ = 1
B. ∫ψ dx = 1
C. ∫|ψ|² dx = 1
D. |ψ| = 1
Answer: C
Rationale: Total probability must equal one.
10.Eigenvalues of a Hermitian operator are
A. Complex
B. Negative
C. Real
D. Zero
Answer: C
Rationale: Observables correspond to real measurement outcomes.
11.The Hamiltonian operator represents
A. Momentum
B. Probability
EXAM QUESTION AND CORRECT
ANSWERS (VERIFIED ANSWERS) PLUS
RATIONALES 2026 Q&A INSTANT
DOWNLOAD PDF
1. The time-dependent Schrödinger equation describes
A. Measurement outcomes
B. Classical trajectories
C. Time evolution of the wavefunction
D. Operator eigenvalues
Answer: C
Rationale: The Schrödinger equation governs how the quantum state evolves in
time.
2. The wavefunction ψ(x,t) represents
A. Charge density
B. Energy density
C. Probability amplitude
D. Particle trajectory
Answer: C
Rationale: The squared magnitude |ψ|² gives probability density.
3. An operator corresponding to momentum in position space is
A. x
B. ∂/∂x
, C. −iħ ∂/∂x
D. ħx
Answer: C
Rationale: Canonical quantization gives momentum as a derivative operator.
4. The expectation value of an observable A is
A. Eigenvalue of A
B. Maximum value of A
C. ⟨ψ|A|ψ⟩
D. Tr(A)
Answer: C
Rationale: Expectation values are inner products with the operator.
5. Operators A and B commute if
A. AB = 0
B. AB = BA
C. A = B
D. A† = B
Answer: B
Rationale: Commutation means the product is order-independent.
6. The uncertainty principle arises from
A. Measurement error
B. Classical noise
C. Non-commuting operators
D. Relativity
Answer: C
Rationale: Operator non-commutation leads to intrinsic uncertainties.
7. The ground state energy of a 1D harmonic oscillator is
A. 0
B. ħω
, C. ½ħω
D. 2ħω
Answer: C
Rationale: Zero-point energy is half a quantum.
8. Ladder operators are useful because they
A. Diagonalize position
B. Remove time dependence
C. Connect energy eigenstates
D. Eliminate uncertainty
Answer: C
Rationale: Creation and annihilation operators raise or lower energy levels.
9. A normalized wavefunction satisfies
A. ψ = 1
B. ∫ψ dx = 1
C. ∫|ψ|² dx = 1
D. |ψ| = 1
Answer: C
Rationale: Total probability must equal one.
10.Eigenvalues of a Hermitian operator are
A. Complex
B. Negative
C. Real
D. Zero
Answer: C
Rationale: Observables correspond to real measurement outcomes.
11.The Hamiltonian operator represents
A. Momentum
B. Probability
