Factorization Method in Quantum Mechanics

By: Shi-Hai Dong

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Hardcover | 10 February 2007

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Hardcover
308 Pages

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23.5 x 15.88 x 1.91

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This book introduces the factorization method in quantum mechanics at an advanced level, with the aim of putting mathematical and physical concepts and techniques like the factorization method, Lie algebras, matrix elements and quantum control at the reader's disposal. For this purpose, the text provides a comprehensive description of the factorization method and its wide applications in quantum mechanics which complements the traditional coverage found in quantum mechanics textbooks.

Industry Reviews

From the reviews:

"An up-to-date organized account of material that can be addressed to an interdisciplinary graduate-level audience. ... Besides the elegance and the effectiveness in characterizing matrix-elements, a motivation for the algebraic approach also relies in the pedagogical expectation that beginners can be better driven to topics like coherent states and supersymmetric Quantum Mechanics. ... The book can be generally addressed to graduate students and young researchers in physics, theoretical chemistry, applied mathematics and electrical engineering ... ." (Giulio Landolfi, Zentralblatt MATH, Vol. 1130 (8), 2008)

"The book under review is an interesting and useful collection of results which fall under the headings of 'factorization method', 'Darboux/Crum transformation', 'supersymmetric quantum mechanics', 'intertwining operator method' and 'shape invariance'. ... can be used by researchers in the field and by students of quantum mechanics. ... the overall impression of the book is that it is useful for a broad audience of physicists and mathematical physicists." (Marek Nowakowski, Mathematical Reviews, Issue 2008 k)

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Introduction
Introduction	p. 3
Method
Theory	p. 15
Lie algebras SU(2) and SU(1,1)	p. 17
Applications in non-relativistic quantum mechanics
Harmonic oscillator	p. 35
Infinitely deep square-well potential	p. 57
Morse potential	p. 73
Poschl-Teller potential	p. 95
Pseudoharmonic oscillator	p. 111
Algebraic approach to an electron in a uniform magnetic field	p. 137
Ring-shaped non-spherical oscillator	p. 143
Generalized Laguerre functions	p. 151
New noncentral ring-shaped potential	p. 157
Poschl-Teller like potential	p. 169
Postition-dependent mass Schrodinger equation for a singular oscillator	p. 177
Applications in relativistic quantum mechanics
SUSYQM and SWKB approach to the Dirac equation with a coulomb potential in 2+1 dimensions	p. 187
Realization of dynamic group for the Dirac hydrogen-like atom in 2+1 dimensions	p. 201
Algebraic approach to Klein-Gordon equation with the hydrogen-like atom in 2+1 dimensions	p. 207
SUSYQM and SWKB approaches to relativistic Dirac and Klein-Gordon equations with hyperbolic potential	p. 213
Quantum control
Controllability of quantum systems for the Morse and PT potentials with dynamic group SU(2)	p. 225
Controllability of quantum system for the PT-like potential with dynamic group SU(1,1)	p. 229
Conclusions and outlooks
Conclusions and outlooks	p. 237
Integral formulas of the confluent hypergeometric functions	p. 239
Mean values [actual symbol not reproducible] for hydrogen-like atom	p. 243
Commutator identities	p. 247
Angular momentum operators in spherical coordinates	p. 249
Confluent hypergeometric function	p. 251
Table of Contents provided by Blackwell. All Rights Reserved.

Factorization Method in Quantum Mechanics

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Hardcover

Industry Reviews

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