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Quasi-Exactly Solvable Models in Quantum Mechanics (Paperback)
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Quasi-Exactly Solvable Models in Quantum Mechanics (Paperback)
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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 Schroedinger 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.
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