GATE Quantum Mechanics: variational method, time independent perturbation theory – Previous Year Questions

6 GATE previous year questions on variational method, time independent perturbation theory (Quantum Mechanics, Physics) with answers and explanations, from every paper.

1. GATE 2022 PH Q39 (2 marks, Multiple choice) – Consider a particle in three different boxes of width L. The potential inside the boxes vary as shown in figures (i), (ii) and (iii) with V଴≪ ħమగమ…
2. GATE 2022 PH Q56 (2 marks, Multiple select) – A 2D square well has n xn y=2(n x x/L)(n y y/L)/L. For perturbation V=Cxy, which statements apply to its first excited state?
3. GATE 2026 PH Q26 (1 mark, Multiple select) – If the perturbation V= x3 is added to the Hamiltonian of a one-dimensional harmonic oscillator, the matrix element m V 0 is/are non-zero for which of…
4. GATE 2025 PH Q44 (2 marks, Multiple choice) – A two-level quantum system has eigenvalues E 1,E 2. A perturbation H= x is introduced, where has energy dimensions, is small and dimensionless, and…
5. GATE 2024 PH Q28 (1 mark, Multiple choice) – Trial functions 1=e-Z(r 1+r 2) and 2=e-Z(r 1+r 2)(1+g r 1- r 2 ) estimate helium ground energy E 0. With variational parameters Z,g and corresponding…
6. GATE 2024 PH Q61 (2 marks, Numerical answer) – A mass m in an infinite well of width a has perturbation V=h2/(40ma2) over 3a/4<x<a, as shown. The first-order shift of its fourth energy eigenstate…