= Quantum bouncer
{title2=$E_n=F\ell z_n,\quad\ell=(\hbar^2/(2mF))^{1/3}$}
A <quantum particle> above a hard reflecting wall in a linearly increasing potential $V(x)=Fx$ for $x>0$. The <Schrödinger equation> reduces to the <Airy equation>. Decay at infinity selects $\operatorname{Ai}$, while the wall requires $\operatorname{Ai}(-z_n)=0$. Thus $\psi_n\propto\operatorname{Ai}(x/\ell-z_n)$ and the energies are the displayed values. The $n$th state has $n-1$ interior nodes and a decaying tail beyond its <classical turning point>. A gravitational realization has $F=mg$; <gravitational neutron bound-state transmission> tests such confinement experimentally.
Back to article page
