Q71 · CSIR NET Chemistry, June 2016
Paper: CSIR NET June 2016 · Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Quantum Chemistry – General · Marks: 2 · Difficulty: Easy
The Hermitian conjugate of operator $d/dx$, called $(d/dx)^{\dagger}$, is actually equal to
(a)$-d/dx$
(b)$d/dx$
(c)$i(d/dx)$
(d)$-i(d/dx)$
Answer
Answer: A ✓ checked by 4AB · confidence high
The source book printed no answer; this one was worked out and checked — see the explanation.
Explanation
Integration by parts gives ∫f*(dg/dx)dx = −∫(df/dx)*g dx for vanishing boundary terms, so (d/dx)† = −d/dx (a). d/dx is anti-Hermitian, and −i d/dx is Hermitian.
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