= Two-dimensional infinite square well
{title2=$E_{nm}=\pi^2\hbar^2(n^2/a^2+m^2/b^2)/(2M)$}
On $0<x<a$, $0<y<b$, with infinite exterior potential, separation of variables gives the normalized eigenbasis
$$
\psi_{nm}=\frac2{\sqrt{ab}}\sin\frac{n\pi x}a\sin\frac{m\pi y}b,\qquad E_{nm}=\frac{\pi^2\hbar^2}{2M}\left(\frac{n^2}{a^2}+\frac{m^2}{b^2}\right),\quad n,m\geq1.
$$
The boundary values vanish and the functions are orthonormal. A general state is a superposition of these products. A degenerate energy eigenspace can contain nonseparable linear combinations of products at the same energy, so a single separated product is not the most general stationary wavefunction in that eigenspace.
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