Factorization method in quantum mechanics
type: Item
instance of: scholarly article
title: Factorization method in quantum mechanics
zbMATH Open document ID: 1130.81001
author: Shi-Hai Dong
published in: Fundamental Theories of Physics
publication date: 2007-03-13T00:00:00Z
review text: In conceiving this book the author realizes that, in spite of its general relevance, there are relatively few tutorial resources dealing with the application of the factorization method to Quantum Mechanical problems. His aim is, therefore, to provide an up-to-date organized account of material that can be addressed to an interdisciplinary graduate-level audience. In doing so, he discusses a number of quantum-mechanical problems of interest in physics and chemistry by paying prior attention to the identification of the first-order ladder operators yielding the Hamiltonian operators into a factorized form, and to the characterization of the dynamical algebras they may form together with other operators. 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 is divided into six Parts: I. Introduction, II. Method, III. Applications in Non-relativistic Quantum Mechanics, IV. Applications in Relativistic Quantum Mechanics, V. Quantum Control, VI. Conclusions and outlooks. In Part I, the author argues on historical development of the subject. Part II simply consists in a couple of pages introducing to the idea underlying the method, and in a chapter giving fundamentals on groups and algebras. Parts III and IV define the actual core of the monograph since they are concerned with the study of explicit problems, and the discussions of the corresponding dynamical algebras of the su(2) and su(1,1) type. Parts III and IV consist in several chapters, each of them considering in some detail a given second-order ordinary differential operator. Chapter headings for parts III and IV are: 4. The harmonic oscillator, 5. The infinitely deep square-well potential, 6. Morse potential, 7. Pösch potential, 8. Pseudoharmonic potential, 9. Algebraic approach to an electron in…
reviewed by: G. Landolfi
Mathematics Subject Classification ID: 81-01
Mathematics Subject Classification ID: 81Q05
Mathematics Subject Classification ID: 81U15
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 81R15
Mathematics Subject Classification ID: 81R05
Mathematics Subject Classification ID: 81Q60
Mathematics Subject Classification ID: 81R30
zbMATH DE Number: 5133445
zbMATH Keywords: Schrödinger equation
zbMATH Keywords: solvable quantum systems
zbMATH Keywords: factorization method
zbMATH Keywords: ladder operators
zbMATH Keywords: dynamic group
zbMATH Keywords: coherent states
zbMATH Keywords: SUSYQM
zbMATH Keywords: shape invariance
zbMATH Keywords: control theory
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5133445