Solution
= Solution
The walls give $\omega=n\pi/(2a)$; normalisation gives $A=1/\sqrt a$, and $E_n=\hbar^2\pi^2n^2/(8ma^2)$. Product-to-sum integration over $(-a,a)$ gives $\langle\psi_n,\psi_m\rangle=\delta_{nm}$.
= Solution
The walls give $\omega=n\pi/(2a)$; normalisation gives $A=1/\sqrt a$, and $E_n=\hbar^2\pi^2n^2/(8ma^2)$. Product-to-sum integration over $(-a,a)$ gives $\langle\psi_n,\psi_m\rangle=\delta_{nm}$.