= Linear ramp state in an infinite square well
{title2=$\psi(x)=\sqrt3x/L^{3/2}$}
The normalized <wavefunction> $\psi(x)=\sqrt3x/L^{3/2}$ on $(0,L)$ has sine coefficients $c_n=(-1)^{n+1}\sqrt6/(n\pi)$. Its <ground-state probability> is $6/\pi^2$, while its <position probability> in $(0,L/3)$ is $1/27$. The constant values of $E_n|c_n|^2$ make its <energy expectation> divergent. It is a valid <Hilbert space> vector but fails the finite-energy Dirichlet boundary-trace condition.
Back to article page
