Dong Shi-Hai. Factorization Method in Quantum Mechanics

Springer, 2007. — 307 p. — (Fundamental Theories of Physics 150). — ISBN13: 978-1-4020-5796-0.This Work introduces the factorization method in quantum mechanics at an advanced level with an aim to put 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 a comprehensive description is provided of the factorization method and its wide applications in quantum mechanics which complements the traditional coverage found in the existing quantum mechanics textbooks. Related to this classic method are the supersymmetric quantum mechanics, shape invariant potentials and group theoretical approaches. It is no exaggeration to say that this method has become the milestone of these approaches. In fact the Author’s driving force has been his desire to provide a comprehensive review volume that includes some new and significant results about the factorization method in quantum mechanics since the literature is inundated with scattered articles in this field, and to pave the Reader’s way into this territory as rapidly as possible. The result: clear and understandable derivations with the necessary mathematical steps included so that the intelligent reader should be able to follow the text with relative ease, in particular when mathematically difficult material is presented.Theory
Lie algebras su(2) and su(1, 1)
Harmonic oscillator
Infinitely deep square-well potential
Morse potential
Pöschl-teller potential
Pseudoharmonic oscillator
Algebraic approach to an electron in a uniform magnetic field
Ring-shaped non-spherical oscillator
New noncentral ring-shaped potential
Pöschl-teller like potential
Position-dependent mass schrödinger equation for a singular oscillator
Susyqm and swkb approach to the dirac equation with a coulomb potential in 2+1 dimensions
Realization of dynamic group for the dirac hydrogen-like atom in 2+1 dimensions
Algebraic approach to klein-gordon equation with the hydrogen-like atom in 2+1 dimensions
Susyqm and swkb approaches to relativistic dirac and klein-gordon equations with hyperbolic potential
Controllability of quantum systems for the morse and pt potentials with dynamic group su(2)
Controllability of quantum system for the pt-like potential with dynamic group su(1, 1)
Conclusions and outlooks