  The non-relativistic Schr\"odinger equation on a domain $\Omega\subset
\mathbb{R}^n$ with boundary is often considered with homogeneous Dirichlet
boundary conditions ($\psi(x)=0$ for $x$ on the boundary) or homogeneous
Neumann boundary conditions ($\partial_n \psi(x)=0$ for $x$ on the boundary and
$\partial_n$ the normal derivative) or Robin boundary conditions
($\partial_n\psi(x)=\alpha\psi(x)$ for $x$ on the boundary and $\alpha$ a real
parameter). Physically, the Dirichlet condition applies if outside of $\Omega$
the potential is much higher than inside (``potential well''). We ask, when
does the Neumann or Robin condition apply physically? Our answer is, when the
potential is much lower (at the appropriate level) in a thin layer before a
potential well, or when a negative delta potential of the appropriate strength
is added close to the potential well.
