| 39B22 | Equations
for real functions |
A. G. Ushveridze, in his monograph ``Quasi-Exactly Solvable Models in
Quantum Mechanics" (IOP Publishing, Bristol, 1994, ISBN: 0750302666),
reviews many models where a ``sufficiently elementary" wave function
(or a finite multiplet of such wave functions) satisfies Schroedinger
equation for a suitably (or ``selfconsistently") determined
interaction. The subject proved interesting in various applications
and one is quite surprised to read that the Lokshin's note in
question (giving precisely a new simple result of this type) cites no
(!) references. Not that this would be perceived as unusual in this
apparently ``almost trivial" context where one picks up ANY wave
function and differentiates it twice. In fact, the Ushveridze's list
of references is also extremely scarce. Still, each of the results of
this type (citing the other authors or not) deserves attention,
especially when it has some non-trivial component in it. This
criterion seems satisfied by the short note in question, where the
``necessary and sufficient" functional-equation relation (1) between
the ansatz and potentials is solved, in Lemma 2, completely. One
feels sorry that due to the above-mentioned connection, the absence
of citations transferred this text from the category of very
interesting contributions to the field to the category of texts which
remain unnoticed by the vast majority of the eligible interested
readers. Especially because the latter argument becomes significantly
strengthened by the parallel closeness of the subject to another
broad area of the so called Calogero-Moser-Sutherland exactly
solvable models and of their Inozemtsev-type partially solvable
generalizations. Let me skip the details here: Reviewers are not
expected to write the extended abstracts which would be much longer
than the papers they re-comment.
title
< "On a family of exactly solvable multiparticle Schr"odinger equations with pair potential.">
keywords
<"N particles on a line; Schroedinger equation; pair potential; ground state; elementary solution; ">
author
<"Lokshin, A.A.">
journal
<"Math. Notes 70, No.1, 137-142; translation from Mat. Zametki 70, No.1, 150-154 (2001). [ISSN 0001-4346]http://www.kluweronline.com/issn/0001-4346/">
|