In quantum chemistry, one-dimensional Schroedinger equation with
Morse potential is of paramount interest since it plays the role of
a popular phenomenological model describing certain important
molecular excitations. For this reason the authors return to this
model (which is exactly solvable) and modify the underlying
mathematics (motivated, e.g., by certain time-dependent
applications) by adding a remote impenetrable barrier to the
potential. Several interesting consequences (e.g., for an externally
driven motion of particles) of this trick are listed, some necessary
related formulae are derived (especially for some currently needed
matrix elements) and a few sample numerical calculations (e.g., of
an escape of particles) are presented. Note added: the message
delivered by the paper looks absurd before one reads the text and
reveals that the title is a bit misleading.
MR2426000 de Lima, Emanuel F.; Ho, Tak-San; Rabitz, Herschel
Solution of the Schrödinger equation for the Morse potential with an
infinite barrier at long range. J. Phys. A 41 (2008), no. 33,
335303, 14 pp. 81Q05 (81U15)