The hermitian conjugate of operator d / d x, called (d / d x), is actually equal to

Q43 · CSIR-NET Chemistry, June 2011

Paper: CSIR-NET June 2011 · Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Postulates Operators · Marks: 2 · Difficulty: Medium

The hermitian conjugate of operator $d / d x$, called $(d / d x)^{\dagger}$, is actually equal to

(a)$-\mathrm{d} / \mathrm{dx}$

(b)d/dx

(c)$i(d/dx)$

(d)$-\mathrm{i}(\mathrm{d} / \mathrm{dx})$

Answer

Answer: A ✓ checked by 4AB · confidence high

Explanation

Integration by parts on ∫f*(dg/dx)dx with vanishing boundary terms gives −∫(df/dx)*g dx, so (d/dx)† = −d/dx: d/dx is anti-Hermitian.

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