Factorization Method in Quantum Mechanics / Fundamental Theories of Physics Bd.150 (PDF)

PART I - Introduction. 1: Introduction. PART II - Method. 2: Theory. 3: Lie Algebras SU(2) and SU(1,1). PART III - Applications in Non-Relativistic Quantum mechanics. 4: Harmonic Oscillator. 5: Infinitely Deep Square-Well Potential. 6: Morse Potential. 7: Pöschl-Teller Potential. 8: Pseudoharmonic Oscillator. 9: Algebraic Approach to an Electron in a Uniform Magnetic Field. 10: Ring-Shaped Non-Spherical Oscillator. 11: Generalized Laguerre Functions. 12: New Non-Central Ring-Shaped Potential. 13: Pöschl-Teller Like Potential. 14: Position-Dependent Mass Schrödinger Equation for a Singular Oscillator. PART IV - Applications in Relativistic Quantum Mechanics. 15: SUSYQM and SKWB Approach to the Dirac Equation with a Coulomb Potential in 2+1 Dimensions. 16: Realization of Dynamic Group for the Dirac Hydrogen-like Atom in 2+1 Dimensions. 17: Algebraic Approach to Klein-Gordon Equation with the Hydrogen-like Atom in 1+2 Dimensions. 18: SUSYQM and SKWB Approaches to Relativistic Dirac and Klein-Gordon Equations with Hyperbolic Potential. PART V - Quantum Control. 19: Controllability of Quantum Systems for the Morse and PT Potentials with Dynamic Group SU(2). 20: Controllability of Quantum System for the PT-like Potential with Dynamic Group SU(1,1). PART VI - Conclusions and Outlooks. 21: Conclusions and outlooks. APPENDICES: A - Integral formulas of the confluent hypergeometric functions. B - Mean values rk for hydrogen-like atom. C - Commutator identities. D - Angular momentum operators in spherical coordinates. E - Confluent hypergeometric function. References. Index.

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)