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.