The function, which is NOT an eigenfunction of the indicated operator, is · ABC26PH0176
Subject: Physical Chemistry · Chapter: Quantum Chemistry · Topic: Quantum Chemistry – General · Exam: CSIR NET 2020 · Marks: 2 · Difficulty: Easy
The function, which is NOT an eigenfunction of the indicated operator, is | Operator | Function |
|---|
| 1. $\dfrac{d^{2}}{dx^{2}}-x^{2}$ | $e^{\frac{-x^{2}}{2}}$ |
| 2. $\dfrac{d^{2}}{dx^{2}}+x^{2}$ | $e^{\frac{-x^{2}}{2}}$ |
| 3. $\dfrac{d^{2}}{dx^{2}}$ | $\cos \dfrac{\pi x}{4}$ |
| 4. $\dfrac{d^{2}}{dx^{2}}$ | $e^{4ix}$ |
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 e^(−x²/2), ψ″ = (x² − 1)ψ. So (d²/dx² + x²)ψ = (2x² − 1)ψ, which is not a multiple of ψ (option 2). The other three pairs are eigenfunction pairs.
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