PHYSICS CANDIDACY EXAM QUESTION
AND CORRECT ANSWERS (VERIFIED
ANSWERS) PLUS RATIONALES 2026 Q&A
INSTANT DOWNLOAD PDF
1. In classical mechanics, a system described by a Lagrangian that does not
explicitly depend on time conserves
A. Linear momentum
B. Angular momentum
C. Energy
D. Action
Answer: C
Rationale: If the Lagrangian has no explicit time dependence, Noether’s theorem
implies conservation of energy.
2. The Poisson bracket {xi, pj} is equal to
A. 0
B. δij/2
C. −δij
D. δij
Answer: D
Rationale: Canonical coordinates satisfy {xi, pj} = δij by definition.
3. A canonical transformation preserves
A. The Hamiltonian
B. The Lagrangian
, C. The form of Hamilton’s equations
D. The action value
Answer: C
Rationale: Canonical transformations preserve the symplectic structure and
Hamilton’s equations.
4. The degeneracy of the nth energy level of a 3D isotropic harmonic oscillator
is
A. n
B. n²
C. (n+1)(n+2)/2
D. 2n+1
Answer: C
Rationale: Degeneracy arises from the number of integer partitions of n among
three dimensions.
5. In quantum mechanics, operators corresponding to observables must be
A. Linear
B. Bounded
C. Hermitian
D. Unitary
Answer: C
Rationale: Hermitian operators ensure real eigenvalues representing measurable
quantities.
6. The commutator [x, px] equals
A. 0
B. −iħ
, C. iħ
D. ħ²
Answer: C
Rationale: This is the fundamental canonical commutation relation.
7. The uncertainty principle ΔxΔp ≥ ħ/2 follows directly from
A. Schrödinger equation
B. Eigenvalue postulate
C. Non-commuting operators
D. Wavefunction normalization
Answer: C
Rationale: The principle arises from operator non-commutativity and the
Cauchy–Schwarz inequality.
8. The ground-state energy of a quantum harmonic oscillator is
A. 0
B. ħω
C. ½ħω
D. 2ħω
Answer: C
Rationale: Zero-point energy remains due to quantum fluctuations.
9. In perturbation theory, the first-order correction to energy depends on
A. Off-diagonal matrix elements
B. Second derivatives of the Hamiltonian
C. Expectation value of the perturbation
D. Transition probabilities
AND CORRECT ANSWERS (VERIFIED
ANSWERS) PLUS RATIONALES 2026 Q&A
INSTANT DOWNLOAD PDF
1. In classical mechanics, a system described by a Lagrangian that does not
explicitly depend on time conserves
A. Linear momentum
B. Angular momentum
C. Energy
D. Action
Answer: C
Rationale: If the Lagrangian has no explicit time dependence, Noether’s theorem
implies conservation of energy.
2. The Poisson bracket {xi, pj} is equal to
A. 0
B. δij/2
C. −δij
D. δij
Answer: D
Rationale: Canonical coordinates satisfy {xi, pj} = δij by definition.
3. A canonical transformation preserves
A. The Hamiltonian
B. The Lagrangian
, C. The form of Hamilton’s equations
D. The action value
Answer: C
Rationale: Canonical transformations preserve the symplectic structure and
Hamilton’s equations.
4. The degeneracy of the nth energy level of a 3D isotropic harmonic oscillator
is
A. n
B. n²
C. (n+1)(n+2)/2
D. 2n+1
Answer: C
Rationale: Degeneracy arises from the number of integer partitions of n among
three dimensions.
5. In quantum mechanics, operators corresponding to observables must be
A. Linear
B. Bounded
C. Hermitian
D. Unitary
Answer: C
Rationale: Hermitian operators ensure real eigenvalues representing measurable
quantities.
6. The commutator [x, px] equals
A. 0
B. −iħ
, C. iħ
D. ħ²
Answer: C
Rationale: This is the fundamental canonical commutation relation.
7. The uncertainty principle ΔxΔp ≥ ħ/2 follows directly from
A. Schrödinger equation
B. Eigenvalue postulate
C. Non-commuting operators
D. Wavefunction normalization
Answer: C
Rationale: The principle arises from operator non-commutativity and the
Cauchy–Schwarz inequality.
8. The ground-state energy of a quantum harmonic oscillator is
A. 0
B. ħω
C. ½ħω
D. 2ħω
Answer: C
Rationale: Zero-point energy remains due to quantum fluctuations.
9. In perturbation theory, the first-order correction to energy depends on
A. Off-diagonal matrix elements
B. Second derivatives of the Hamiltonian
C. Expectation value of the perturbation
D. Transition probabilities
