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GATE 2021 CY – Question 26

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. · 1 mark · Multiple select

Acceptable wavefunctions for a quantum particle must be:

  1. odd
  2. even
  3. single-valued
  4. continuous

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Correct answer: (C) single-valued; (D) continuous

Explanation

A wavefunction must assign one complex amplitude to each position, so it is single-valued. For the ordinary finite-potential problems intended here, it must also be continuous; discontinuities would generate inadmissible kinetic-energy behaviour. Oddness and evenness are possible parity properties in symmetric potentials, not universal requirements. **C,D**.