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GATE 2023 CY – Question 45

Physical Chemistry · Structure: Postulates of quantum mechanics. Operators. Commutation relations and expectations values; the role of the wave function and its absolute squares, time dependent and time independent Schrödinger equations. Born interpretation. Dirac bra-ket notation. Examples of model solvable quantum mechanical systems. · 2 marks · Multiple choice

Match Column I functions with Column II quantum systems.

P. Associated Legendre polynomials

Q. Hermite polynomials

R. Associated Laguerre polynomials

S. Trigonometric functions

I. Harmonic oscillator

II. Particle in a box

III. Angular part of H atom

IV. Radial part of H atom

  1. P→III, Q→I, R→IV, S→II
  2. P→III, Q→IV, R→II, S→I
  3. P→IV, Q→I, R→III, S→II
  4. P→II, Q→III, R→IV, S→I

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Correct answer: (A) P→III, Q→I, R→IV, S→II

Explanation

Hydrogen’s angular equation contains associated Legendre polynomials; its radial equation contains associated Laguerre polynomials. The harmonic oscillator uses Hermite polynomials, and the infinite box uses trigonometric eigenfunctions.

Thus P→III, Q→I, R→IV, S→II,**A**.