Half-line finite well
= Half-line finite well
A one-dimensional well $V=-V_0$ on $0<x<a$, with an infinite wall at zero and $V=0$ beyond $a$. For $-V_0<E<0$, the interior <wavefunction> is proportional to $\sin kx$ and the exterior decays as $e^{-qx}$. Continuity gives $k\cot ka=-q$, where $k^2=2m(E+V_0)/\hbar^2$ and $q^2=-2mE/\hbar^2$. Its <half-line finite-well bound-state count> has a nonzero minimum depth, unlike a full-line attractive one-dimensional well.