Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2022 / Paper 4 / 59 / b / ii

The probability density $|{\psi }_n(x){|}^2$ is symmetric about $a/2$, while $x-a/2$ is antisymmetric. ThereforeThe use of a midpoint-zero electric potential matters: adding a constant potential would add the corresponding uniform energy shift.