Q46 · CSIR-NET Chemistry, June 2011
Paper: CSIR-NET June 2011 · Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Postulates Operators · Marks: 2 · Difficulty: Medium
An operator A is defined as $A=-\frac{d}{d x}+x$. Which one of the following statements is true?
(a)A is a Hermitian operator.
(b)$\mathrm{A}^{\dagger}$ is an antihermitian operator.
(c)Both $AA^{\dagger}$ and $A^{\dagger}A$ are Hermitian.
(d)$AA^{\dagger}$ is Hermitian, but $A^{\dagger}A$ is antihermitian
Answer
Answer: C ✓ checked by 4AB · confidence high
Explanation
A = −d/dx + x is neither Hermitian nor anti-Hermitian (A† = d/dx + x), but any product of the form AA† or A†A is Hermitian (c).
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