7.6 Exercise 31

Suppose an infinite square well extends from $− L / 2$ to $+ L / 2$. Solve the time-independent Schrӧdinger’s equation to find the allowed energies and stationary states of a particle with mass m that is confined to this well. Then show that these solutions can be obtained by making the coordinate transformation $x ′ = x - L / 2$ for the solutions obtained for the well extending between 0 and L.