Zentralblatt MATH - REVIEW SUBMISSION FORM

Zentralblatt MATH HOME

Your review has been received.

Thank you very much.

(You may want so save a copy of this page for your files.)

Name:

Miloslav Znojil

Reviewer number:

9689

Email:

znojil@ujf.cas.cz

Item's zbl-Number:

DE 0165 24 655

Author(s):

Gohberg, I.; Kaashoek, M. A.; Sakhnovich, A. L.:

Shorttitle:

Bound states of a canconical system with a pseudo-exponential potential

Source:

Integral Equations Oper. Theory 40, No. 3, 268 - 277 (2001).

Classification:

34L05

General spectral theory

34A55

Inverse problems

34A05

Explicit solutions and reductions

34B20

Weyl theory and its generalizations

47N20

Applications to differential and integral equations

Primary Classification:

Secondary Classification:

Keywords:

canonical systems; pseudo-exponential potential; pseudo-Dirac self-adjoint operator; all bound states in closed form; half-line and full-line axis of coordinates;

Review:

Non-relativistic quantum mechanics attracts attention to the so
called bound state solutions of the ordinary linear differential
equations of the second order. Many of these solutions may be
obtained in closed form, and also a relativistic counterpart of
the bound state problem remains often solvable. On this
background, the paper returns to some older results (by the same
authors, quoted as refs. [5] and [6]) which proposed and studied a
certain matrix, m-dimensional generalization of the equations of
quantum mechanics containing the so called pseudo-exponential
matrix potentials. Basically, the paper offers a new theorem on
the bound state solutions (in both its half-line and full-line
versions) making the old results (formulated in the language of
spectral function) more explicit, especially in the questions
concerning the multiplicity of the eigenvalues or the explicit
form of the eigenfunctions.

Remarks to the editors:

(New formular )