= Solution
The <parity> of a <wavefunction> is its <eigenvalue> under <spatial reflection>: $\psi(-x)=+\psi(x)$ for <even function>[even] parity and $\psi(-x)=-\psi(x)$ for <odd function>[odd] parity. If $V(-x)=V(x)$, the <Hamiltonian operator>[Hamiltonian] commutes with reflection, so its <energy eigenspaces> admit a parity <eigenbasis>. In particular, every <nondegenerate energy eigenvalue>[nondegenerate] bound-state <eigenstate>[energy eigenfunction] has definite parity; within a <state degeneracy>[degenerate] scattering eigenspace one must choose the even and odd <linear combinations>.
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