Title: Exactly solvable Schrödinger equation with double-well potential for hydrogen bond,
Abstract: We construct a double-well potential for which the Schrödinger equation can
be exactly solved via reducing to the confluent Heun's one. Thus the wave
function is expressed via the confluent Heun's function. The latter is
tabulated in {\sl {Maple}} so that the obtained solution is easily treated. The
potential is infinite at the boundaries of the final interval that makes it to
be highly suitable for modeling hydrogen bonds (both ordinary and low-barrier
ones). We exemplify theoretical results by detailed treating the hydrogen bond
in $KHCO_3$ and show their good agreement with literature experimental data.