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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