Factorization Method in Quantum Mechanics

• METHOD.- THEORY.- LIE ALGEBRAS SU(2) AND SU(1, 1).- APPLICATIONS IN NON-RELATIVISTIC QUANTUM MECHANICS.- 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.- GENERALIZED LAGUERRE FUNCTIONS.- NEW NONCENTRAL RING-SHAPED POTENTIAL.- PÖSCHL-TELLER LIKE POTENTIAL.- POSITION-DEPENDENT MASS SCHRÖDINGER EQUATION FOR A SINGULAR OSCILLATOR.- APPLICATIONS IN RELATIVISTIC QUANTUM MECHANICS.- 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.- QUANTUM CONTROL.- 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.- CONCLUSIONS AND OUTLOOKS.

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)