Geodesic
Isolated solutions of~a~local polaron model
Teoretičeskaâ i matematičeskaâ fizika, Tome 80 (1989) no. 3, pp. 399-404

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A simple local polaron model is studied. The Schrödinger equation for the model in the holomorphic representation is reduced to the system of the first order differential equations. The eigen-values are determined from the condition that the solution belongs to the class of holomorphic functions. In the general case, the eigen-values are found from a certain transcendental equation including continuous fraction. On the basis of the general theory of differential equations algebraic equations are obtained for the eigen-vectors of the simplest isolated solutions. Possibility of intersection of eigenvalues in isolated points is demonstrated. Impossibility of phase transition for the simple local polaron model is rigorously proved. 
@article{TMF_1989_80_3_a7,
     author = {A. I. Volokitin},
     title = {Isolated solutions of~a~local polaron model},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {399--404},
     publisher = {mathdoc},
     volume = {80},
     number = {3},
     year = {1989},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1989_80_3_a7/}
}
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A. I. Volokitin. Isolated solutions of~a~local polaron model. Teoretičeskaâ i matematičeskaâ fizika, Tome 80 (1989) no. 3, pp. 399-404. http://geodesic.mathdoc.fr/item/TMF_1989_80_3_a7/