COMPREHENSIVE PHYSICS QUALIFYING
EXAM (PHD QUALIFIER – UNIVERSITY-
BASED) QUESTION AND CORRECT
ANSWERS (VERIFIED ANSWERS) PLUS
RATIONALES 2026 Q&A INSTANT
DOWNLOAD PDF
1. The Lagrangian for a free relativistic particle is proportional to
A. 𝑚𝑣 2 /2
B. 𝑚𝑐 2 √1 − 𝑣 2 /𝑐 2
C. −𝑚𝑐 2 √1 − 𝑣 2 /𝑐 2
D. 𝑚𝑐 2 (1 − 𝑣 2 /𝑐 2 )
Answer: C
Rationale: The relativistic action is −𝑚𝑐 2 ∫ 𝑑𝑠, giving the Lagrangian
−𝑚𝑐 2 √1 − 𝑣 2 /𝑐 2 .
2. The Poisson bracket {𝑞𝑖 , 𝑝𝑗 }equals
A. 0
B. 𝛿𝑖𝑗
C. −𝛿𝑖𝑗
D. 1/2𝛿𝑖𝑗
Answer: B
Rationale: Canonical coordinates satisfy {𝑞𝑖 , 𝑝𝑗 } = 𝛿𝑖𝑗 .
3. A conserved quantity corresponds to
A. Time dependence of Hamiltonian
, B. Gauge choice
C. Continuous symmetry
D. Boundary condition
Answer: C
Rationale: Noether’s theorem links continuous symmetries to conservation
laws.
4. The Hamiltonian of a simple harmonic oscillator equals
A. 𝑝2 /2𝑚 + 𝑘𝑥 2
B. 𝑝2 /2𝑚 + 𝑘𝑥 2 /2
C. 𝑝2 /𝑚 + 𝑘𝑥 2
D. 𝑝2 /2𝑘 + 𝑚𝑥 2
Answer: B
Rationale: The potential energy is 𝑘𝑥 2 /2, giving the standard
Hamiltonian.
5. The action has dimensions of
A. Energy
B. Momentum
C. Energy × time
D. Force × length
Answer: C
Rationale: Action has units of joule-seconds, same as angular momentum.
6. The commutator [𝑥 , 𝑝]in quantum mechanics equals
A. 0
B. 𝑖ℏ
C. −𝑖ℏ
D. ℏ2
Answer: B
Rationale: Canonical commutation relation defines quantum mechanics.
, 7. The ground state energy of a 1D harmonic oscillator is
A. 0
B. ℏ𝜔
C. ℏ𝜔/2
D. 2ℏ𝜔
Answer: C
Rationale: Zero-point energy arises from uncertainty principle.
8. Operators corresponding to observables must be
A. Unitary
B. Hermitian
C. Anti-Hermitian
D. Real
Answer: B
Rationale: Hermitian operators have real eigenvalues.
9. Degeneracy occurs when
A. Eigenvalues are complex
B. Two states share an eigenvalue
C. Wavefunctions vanish
D. Operators commute
Answer: B
Rationale: Degeneracy means multiple eigenstates with same eigenvalue.
10.Measurement collapses the wavefunction to
A. Superposition
B. Energy eigenstate
C. An eigenstate of measured observable
D. Ground state
Answer: C
Rationale: Postulate of quantum measurement.
EXAM (PHD QUALIFIER – UNIVERSITY-
BASED) QUESTION AND CORRECT
ANSWERS (VERIFIED ANSWERS) PLUS
RATIONALES 2026 Q&A INSTANT
DOWNLOAD PDF
1. The Lagrangian for a free relativistic particle is proportional to
A. 𝑚𝑣 2 /2
B. 𝑚𝑐 2 √1 − 𝑣 2 /𝑐 2
C. −𝑚𝑐 2 √1 − 𝑣 2 /𝑐 2
D. 𝑚𝑐 2 (1 − 𝑣 2 /𝑐 2 )
Answer: C
Rationale: The relativistic action is −𝑚𝑐 2 ∫ 𝑑𝑠, giving the Lagrangian
−𝑚𝑐 2 √1 − 𝑣 2 /𝑐 2 .
2. The Poisson bracket {𝑞𝑖 , 𝑝𝑗 }equals
A. 0
B. 𝛿𝑖𝑗
C. −𝛿𝑖𝑗
D. 1/2𝛿𝑖𝑗
Answer: B
Rationale: Canonical coordinates satisfy {𝑞𝑖 , 𝑝𝑗 } = 𝛿𝑖𝑗 .
3. A conserved quantity corresponds to
A. Time dependence of Hamiltonian
, B. Gauge choice
C. Continuous symmetry
D. Boundary condition
Answer: C
Rationale: Noether’s theorem links continuous symmetries to conservation
laws.
4. The Hamiltonian of a simple harmonic oscillator equals
A. 𝑝2 /2𝑚 + 𝑘𝑥 2
B. 𝑝2 /2𝑚 + 𝑘𝑥 2 /2
C. 𝑝2 /𝑚 + 𝑘𝑥 2
D. 𝑝2 /2𝑘 + 𝑚𝑥 2
Answer: B
Rationale: The potential energy is 𝑘𝑥 2 /2, giving the standard
Hamiltonian.
5. The action has dimensions of
A. Energy
B. Momentum
C. Energy × time
D. Force × length
Answer: C
Rationale: Action has units of joule-seconds, same as angular momentum.
6. The commutator [𝑥 , 𝑝]in quantum mechanics equals
A. 0
B. 𝑖ℏ
C. −𝑖ℏ
D. ℏ2
Answer: B
Rationale: Canonical commutation relation defines quantum mechanics.
, 7. The ground state energy of a 1D harmonic oscillator is
A. 0
B. ℏ𝜔
C. ℏ𝜔/2
D. 2ℏ𝜔
Answer: C
Rationale: Zero-point energy arises from uncertainty principle.
8. Operators corresponding to observables must be
A. Unitary
B. Hermitian
C. Anti-Hermitian
D. Real
Answer: B
Rationale: Hermitian operators have real eigenvalues.
9. Degeneracy occurs when
A. Eigenvalues are complex
B. Two states share an eigenvalue
C. Wavefunctions vanish
D. Operators commute
Answer: B
Rationale: Degeneracy means multiple eigenstates with same eigenvalue.
10.Measurement collapses the wavefunction to
A. Superposition
B. Energy eigenstate
C. An eigenstate of measured observable
D. Ground state
Answer: C
Rationale: Postulate of quantum measurement.
