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Name:  
Miloslav Znojil  
Reviewer number:  
9689  
Email:  
znojil@ujf.cas.cz  
Item's zblNumber:  
DE 0165 24 655  
Author(s):  
Gohberg, I.; Kaashoek, M. A.; Sakhnovich, A. L.:  
Shorttitle:  
Bound states of a canconical system with a pseudoexponential potential  
Source:  
Integral Equations Oper. Theory 40, No. 3, 268  277 (2001).  
Classification:  
 
Primary Classification:  
Secondary Classification:  
Keywords:  
canonical systems; pseudoexponential potential; pseudoDirac selfadjoint operator; all bound states in closed form; halfline and fullline axis of coordinates;  
Review:  
Nonrelativistic 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, mdimensional generalization of the equations of quantum mechanics containing the so called pseudoexponential matrix potentials. Basically, the paper offers a new theorem on the bound state solutions (in both its halfline and fullline 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:  