UPSC Combined Geo-Scientist, Mains · 2025 · Mains Paper II

Q14. Hermitian character of cÂ and of Â + B̂

20 marks
Topic: Quantum chemistry
Question only

Question

Let Â and B̂ be Hermitian operators and c be a constant. (a) Show that cÂ is Hermitian if c is a real number and cÂ is not Hermitian if c is not a real number. (b) Show that (Â + B̂) is Hermitian.

Model answer

The free solution for 2025 answers questions 1, 2, 4, 5, 6, 7, 10, 11, 12 and 13, the ones picked in its time plan. Question 14 is answered in full in the Geo-Scientist Chemistry Paper II, 2021 to 2025 book, with every part of every paper.

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UPSC Combined Geo-Scientist (Main) Chemistry Paper II: Model Answers 2021 to 2025

All fifteen questions of each paper, with the question printed above its answer
Numericals worked from formula to result with units; graphs with labelled axes
Topic-wise weightage and a topic-wise index

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Topic notes: the postulates of quantum mechanics, operators, eigenfunctions, Hermitian operators and acceptable wave functions, with every Civil Services, IFoS and Geo-Scientist PYQ →

CoversHermitian operatorquantum mechanical operatorscomplex conjugatereal eigenvaluessum of operators