Selected MCQ

Current Question
The ground state energy of a quantum harmonic oscillator is:
  • A. Zero
  • B. (\frac{1}{2}h\nu)
  • C. (h\nu)
  • D. Infinite
Correct Answer: B
Explanation:
Zero-point energy is half quantum energy.
Related Question 1
In a Hilbert space formulation of quantum mechanics, physical states are represented by:
  • A. Real numbers
  • B. Vectors up to a global phase
  • C. Scalars only
  • D. Matrices only
Correct Answer: B
Explanation:
States are rays in Hilbert space, invariant under global phase.
Related Question 2
Which principle states that identical fermions cannot occupy the same quantum state?
  • A. Heisenberg principle
  • B. Pauli exclusion principle
  • C. Hund’s rule
  • D. Aufbau principle
Correct Answer: B
Explanation:
Fermions obey antisymmetric wavefunctions prohibiting identical states.
Related Question 3
Which statement about simple harmonic motion is correct?
  • A. Acceleration is proportional to displacement and in the same direction
  • B. Velocity is maximum at extreme position
  • C. Total energy varies sinusoidally
  • D. Acceleration is proportional to displacement and opposite in direction
Correct Answer: D
Explanation:
SHM requires a restoring acceleration opposite to displacement.
Related Question 4
For a damped harmonic oscillator, critical damping corresponds to:
  • A. Fastest return to equilibrium without oscillation
  • B. Largest amplitude oscillation
  • C. Zero restoring force
  • D. Constant total energy
Correct Answer: A
Explanation:
Critical damping is the threshold between oscillatory and non-oscillatory motion with minimum settling time.
Related Question 5
In the canonical ensemble, the probability of a microstate with energy (E_i) is proportional to:
  • A. (e^{+E_i/kT})
  • B. (e^{-E_i/kT})
  • C. (E_i/kT)
  • D. (1/E_i)
Correct Answer: B
Explanation:
The Boltzmann factor assigns lower probability to higher-energy microstates.