GATE Quantum Mechanics: addition of angular momenta – Previous Year Questions

5 GATE previous year questions on addition of angular momenta (Quantum Mechanics, Physics) with answers and explanations, from every paper.

1. GATE 2022 PH Q21 (1 mark, Multiple select) – Which pairs of orbital and total angular momentum operators commute?
2. GATE 2023 PH Q52 (2 marks, Multiple choice) – Two nonidentical spin-half particles are in . For H=4 S 1 S 2/2, what is the energy expectation?
3. GATE 2026 PH Q40 (2 marks, Multiple choice) – Consider two particles with angular momenta j 1=2 and j 2=/2. If the expression j=5/2,m=3/2=c 1 j 1=2,m 1=1 j 2=1/2,m 2=1/2+c 2 j 1=2,m 1=2 j 2=1/2,m…
4. GATE 2026 PH Q59 (2 marks, Numerical answer) – The Hamiltonian of two interacting spin-1/2 particles is H=(A/2) S 1 S 2, where S 1 and S 2 are the spin angular momenta of particles 1 and 2,…
5. GATE 2025 PH Q46 (2 marks, Multiple choice) – Three non-identical spin-half particles have Hamiltonian H= A2( S 1+ S 2) S 3, where the spin operators label particles 1,2,3 and A has appropriate…