Selected MCQ

Current Question
The partition function in statistical mechanics encodes:
  • A. Only energy levels
  • B. All thermodynamic information
  • C. Only entropy
  • D. Only pressure
Correct Answer: B
Explanation:
Thermodynamic quantities can be derived from the partition function.
Related Question 1
The partition function (Z) is related to Helmholtz free energy (F) by:
  • A. (F = kT \ln Z)
  • B. (F = -kT \ln Z)
  • C. (F = Z/kT)
  • D. (F = k/Z)
Correct Answer: B
Explanation:
Helmholtz free energy derives from partition function logarithm.
Related Question 2
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 3
Which functional group is alcohol?
  • A. -COOH
  • B. -OH
  • C. -NH₂
  • D. -CHO
Correct Answer: B
Explanation:
Alcohols contain hydroxyl group.
Related Question 4
In quantum mechanics, the commutator ([x,p]) equals:
  • A. 0
  • B. (i\hbar)
  • C. (-i\hbar)
  • D. (\hbar^2)
Correct Answer: B
Explanation:
Position and momentum operators satisfy ([x,p]=i\hbar).
Related Question 5
In quantum mechanics, expectation value of an observable corresponds to:
  • A. Most probable value
  • B. Average measurement over many identical systems
  • C. Minimum energy
  • D. Maximum probability
Correct Answer: B
Explanation:
Expectation value is statistical mean of repeated measurements.