This book is concerning to a Differential Galois (Picard-Vessiot) Theory point of view of the Supersymmetric Quantum Mechanics. The main object is the non-relativistic stationary Schrödinger equation , where are introduced the concepts of Algebraic Spectrum and Hamiltonian Algebrization. Using the Kovacic's Algorithm and the Hamiltonian Algebrization are analyzed Darboux transformations, Crum iterations and supersymmetric quantum mechanics, including their Algebrized Versions from a Galoisian approach. In particular are obtained the ground state, eigenvalues, eigenfunctions, the differential Galois groups and eigenrings of some Schrödinger equations with potentials such as exactly solvable, quasi-exactly solvable and shape invariant potentials. Finally is introduced one methodology to find Algebraically Solvable and Algebraically Quasi- Solvable Potentials. It consists in to apply the Hamiltonian Algebrization, as inverse process, over families of second order linear differential equations integrables in the Picard-Vessiot sense for a set of parameters, in particular, involving orthogonal polynomials and special functions.
Galoisian Approach to Supersymmetric Quantum Mechanics
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Description
This book is concerning to a Differential Galois (Picard-Vessiot) Theory point of view of the Supersymmetric Quantum Mechanics. The main object is the non-relativistic stationary Schrödinger equation , where are introduced the concepts of Algebraic Spectrum and Hamiltonian Algebrization. Using the Kovacic's Algorithm and the Hamiltonian Algebrization are analyzed Darboux transformations, Crum iterations and supersymmetric quantum mechanics, including their Algebrized Versions from a Galoisian approach. In particular are obtained the ground state, eigenvalues, eigenfunctions, the differential Galois groups and eigenrings of some Schrödinger equations with potentials such as exactly solvable, quasi-exactly solvable and shape invariant potentials. Finally is introduced one methodology to find Algebraically Solvable and Algebraically Quasi- Solvable Potentials. It consists in to apply the Hamiltonian Algebrization, as inverse process, over families of second order linear differential equations integrables in the Picard-Vessiot sense for a set of parameters, in particular, involving orthogonal polynomials and special functions.
We have written this book in order to provide a single compact source for undergraduate and graduate students, as well as for professional physicists who want to understand the essentials of...
This is the first volume in a series of books on the general theme of Supersymmetric Mechanics; the series is based on lectures and discussions held in 2005 and 2006 at the INFN-Laboratori Nazionali...
The idea of supersymmetry was originally introduced in relativistic quantum field theories as a generalization of Poincare symmetry. In 1976 Nicolai sug gested an analogous generalization for...
We read in order to know we are not alone, I once heard, and perhaps it could also be suggested that we write in order not to be alone, to endorse, to promote continuity. The idea for this book took...
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