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UPSC Combined Geo-Scientist

Chemist

  • 3 descriptive papers
  • 200 marks each
  • 3 h per paper

Mains Paper II covers physical chemistry.

UPSC Combined Geo-Scientist, Mains · 2024 · Mains Paper II

Q8. i d/dx is Hermitian, d/dx is not

Question

Prove that the operator i d/dx is Hermitian, but d/dx is not.

Answer in brief

Integration by parts turns ∫f* (dg/dx) dx into −∫g (df/dx)* dx: d/dx fails the test by a sign (anti-Hermitian); the factor i, with i* = −i, restores the sign, so i d/dx is Hermitian.

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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 operatoranti-Hermitianintegration by partsmomentum operatorquantum operators