If A and B are non-commuting hermitian operators, all eigenvalues of the operator given by the commutator [A… · ABC26PH0138

Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Postulates Operators · Exam: CSIR NET 2012 · 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

Explanation

For Hermitian A and B, [A,B]† = −[A,B]: the commutator is anti-Hermitian, so its eigenvalues are purely imaginary (c).

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