GATE Quantum Mechanics: linear vectors and operators in Hilbert space – Previous Year Questions

3 GATE previous year questions on linear vectors and operators in Hilbert space (Quantum Mechanics, Physics) with answers and explanations, from every paper.

1. GATE 2022 PH Q40 (2 marks, Multiple choice) – Which is Hermitian in cylindrical coordinates (s,phi,z)?
2. GATE 2026 PH Q13 (1 mark, Multiple choice) – Consider an operator A which is not Hermitian. Find the possible values of c and d such that the operator (c A-d A) is Hermitian.
3. GATE 2026 PH Q51 (2 marks, Multiple select) – Consider two operators A and B which are related as A=(i B). If is a non-zero real number, which of the following statements is/are true?