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Quasi-Exactly Solvable Models in Quantum Mechanics (Hardcover)
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Quasi-Exactly Solvable Models in Quantum Mechanics (Hardcover)
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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 Schrodinger 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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