Question Bank NAT • 2 Marks Section 4: Quantum Mechanics Perturbation theory

QB_PH_097: Perturbation theory

Question Statement

A particle in a 1D box ($0 \le x \le L$) in ground state $\psi_1(x) = \sqrt{\frac{2}{L}} \sin(\frac{\pi x}{L})$ is perturbed by $H' = V_0 \delta(x - L/2)$. The first-order shift $E_1^{(1)}$ in units of $V_0 / L$ is:
Correct Answer
2, 2
Verified Key

Step-by-Step KaTeX Derivation & Detailed Explanation

### Solution: $E_1^{(1)} = \frac{2}{L}\sin^2(\pi/2) V_0 = \frac{2V_0}{L}$.
← Prev (QB_PH_096) Next (QB_PH_098) →

Practice In Authentic CBT Exam Interface

Test your skills under authentic timed conditions with live scoring and official TCS iON calculator.

Launch CBT Mock Test