Q93 · CSIR NET Chemistry, December 2012
Paper: CSIR NET December 2012 · Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Postulates Operators · Marks: 2 · Difficulty: Medium
If A and B are non-commuting Hermitian operators, all eigenvalues of the operator given by the commutator [A, B] are
(a)complex
(b)real
(c)imaginary
(d)zero
Answer
Answer: C ✓ checked by 4AB · confidence high
The source book printed no answer; this one was worked out and checked — see the explanation.
Explanation
For Hermitian A and B, [A, B]† = −[A, B]: the commutator is anti-Hermitian, so its eigenvalues are purely imaginary (e.g. [x, p] = iħ).
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