Q95 · CSIR NET Chemistry, June 2016
Paper: CSIR NET June 2016 · Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Postulates Operators · Marks: 2 · Difficulty: Medium
The function, which is NOT an eigenfunction of the indicated operator, is
| Operator | Function |
|---|---|
| 1. $\frac{d^{2}}{dx^{2}}-x^{2}$ | $e^{\frac{-x^{2}}{2}}$ |
| 2. $\frac{d^{2}}{dx^{2}}+x^{2}$ | $e^{\frac{-x^{2}}{2}}$ |
| 3. $\frac{d^{2}}{dx^{2}}$ | $\cos\frac{\pi x}{4}$ |
| 4. $\frac{d^{2}}{dx^{2}}$ | $e^{4ix}$ |
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
For ψ = e^(−x²/2), ψ'' = (x² − 1)ψ. So (d²/dx² − x²)ψ = −ψ, an eigenfunction, but (d²/dx² + x²)ψ = (2x² − 1)ψ is not (option 2). cos(πx/4) and e^(4ix) are eigenfunctions of d²/dx².
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