For any operator A and its adjoint A, the INCORRECT statement is:

Q80 · CSIR-NET Chemistry, June 2012

Paper: CSIR-NET June 2012 · Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Postulates Operators · Marks: 2 · Difficulty: Easy

For any operator A and its adjoint $\mathrm{A}^{\dagger}$, the INCORRECT statement is:

(a)$\mathrm{AA}^{\dagger}$ is Hermitian

(b)$\mathrm{AA}^{\dagger}+\mathrm{A}^{\dagger} \mathrm{A}$ is hermitian.

(c)$\mathrm{A}+\mathrm{A}^{\dagger}$ is Hermitian

(d)$\mathrm{A}-\mathrm{A}^{\dagger}$ is Hermitian

Answer

Answer: D ✓ checked by 4AB · confidence high

The source book printed no answer; this one was worked out and checked — see the explanation.

Explanation

(A − A†)† = A† − A = −(A − A†): the difference is anti-Hermitian. AA†, A†A + AA† and A + A† are all Hermitian.

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