Q108 · CSIR-NET Chemistry, December 2011

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

Identify which of the following operators is not hermitian?

(a)$\frac{\hbar}{\mathrm{i}} \frac{\mathrm{d}}{\mathrm{dx}}$

(b)$\mathrm{i} \frac{\mathrm{d}^{2}}{\mathrm{dx}^{2}}$

(c)$\frac{\mathrm{d}^{2}}{\mathrm{dx}^{2}}$

(d)$x^{2}$

Answer

Answer: B ✓ checked by 4AB · confidence high

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

Explanation

d²/dx² is Hermitian, so i·d²/dx² is anti-Hermitian (its expectation values are imaginary); (ħ/i)d/dx is the momentum operator and x² is real.

Study loop for Quantum Chemistry