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GATE 2019 CY – Question 43

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

A one-dimensional system has $\psi=\sin(kx)e^{3ikx}$. Which is a possible result of a momentum measurement?

  1. 0
  2. $\hbar k$
  3. $2\hbar k$
  4. $3\hbar k$

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Correct answer: (C) $2\hbar k$

Explanation

Write $\sin kx=(e^{ikx}-e^{-ikx})/(2i)$. Then ψ is proportional to $e^{4ikx}-e^{2ikx}$. Plane waves e^(iqx) are momentum eigenstates with eigenvalue ℏq, giving possible values 4ℏk and 2ℏk. Only 2ℏk appears among the options: C.

More 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. questions

All 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. questions →