Past exam of the quantum theory course of the University of Oxford / 2021 / 1 / c / iv

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- Solution iv

Solution

The parity operator exchanges

ψ_{n}

and

ψ_{- n}

. Their coefficients in the wavefunction are equal, so

(R Ψ) (x, t) = Ψ (- x, t) = \frac{1 + e ^{- i Ω t} c o s ( - 2 x )}{3 π} = Ψ (x, t) .

Thus the wavefunction is a parity operator eigenstate with eigenvalue

+ 1

at every time. The orthogonal projection onto the

- 1

(I - R) /2

, which annihilates it. By the Born rule,

Pr (R = - 1) = 0.

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