= Central delta barrier in a symmetric infinite well
{title2=$\tan(\lambda a)=-\hbar^2\lambda/(m\kappa)$}
Inside walls at $\pm a$, a central <delta potential> of strength $\kappa$ leaves odd <parity operator> eigenstates unchanged because their wavefunctions vanish at zero. For even states, continuity and the derivative jump $\psi'(0+)-\psi'(0-)=2m\kappa\psi(0)/\hbar^2$ give the displayed quantization equation. For $\kappa>0$, one root lies between $(n+1/2)\pi/a$ and $(n+1)\pi/a$ for every $n\ge0$.
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