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Quasi-Exactly Solvable Models in Quantum Mechanics - A. G. Ushveridze

Quasi-Exactly Solvable Models in Quantum Mechanics

Hardcover Published: 5th September 2000
ISBN: 9780750302661
Number Of Pages: 465

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Exactly solvable models, that is, models with explicitly and completely diagonalizable Hamiltonians are too few in number and insufficiently diverse to meet the requirements of modern quantum physics. Quasi-exactly solvable (QES) models (whose Hamiltonians admit an explicit diagonalization only for some limited segments of the spectrum) provide a practical way forward.
Although QES models are a recent discovery, the results are already numerous. Collecting the results of QES models in a unified and accessible form, Quasi-Exactly Solvable Models in Quantum Mechanics provides an invaluable resource for physicists using quantum mechanics and applied mathematicians dealing with linear differential equations. By generalizing from one-dimensional QES models, the expert author constructs the general theory of QES problems in quantum mechanics. He describes the connections between QES models and completely integrable theories of magnetic chains, determines the spectra of QES SchrAdinger equations using the Bethe-Iansatz solution of the Gaudin model, discusses hidden symmetry properties of QES Hamiltonians, and explains various Lie algebraic and analytic approaches to the problem of quasi-exact solubility in quantum mechanics.
Because the applications of QES models are very wide, such as, for investigating non-perturbative phenomena or as a good approximation to exactly non-solvable problems, researchers in quantum mechanics-related fields cannot afford to be unaware of the possibilities of QES models.

Preface
Acknowledgments
Quasi-exact solvability. What does that mean?p. 1
Simplest analytic methods for constructing quasi-exactly solvable modelsp. 82
The inverse method of separation of variablesp. 150
Classification of quasi-exactly solvable models with separable variablesp. 247
Completely integrable Gaudin models and quasi-exact solvabilityp. 322
App. A The inverse Schrodinger problem and its solution for several given statesp. 394
App. B The generalized quantum tops and exact solvabilityp. 406
App. C The method of raising and lowering operatorsp. 412
App. D Lie-algebraic hamiltonians and quasi-exact solvabilityp. 432
Referencesp. 453
Indexp. 458
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780750302661
ISBN-10: 0750302666
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 465
Published: 5th September 2000
Publisher: INST OF PHYSICS PUB
Country of Publication: GB
Dimensions (cm): 24.77 x 16.51  x 3.18
Weight (kg): 0.91
Edition Number: 1

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