skip to main content

Title: Supersymmetric quantum mechanics and Painlevé equations

In these lecture notes we shall study first the supersymmetric quantum mechanics (SUSY QM), specially when applied to the harmonic and radial oscillators. In addition, we will define the polynomial Heisenberg algebras (PHA), and we will study the general systems ruled by them: for zero and first order we obtain the harmonic and radial oscillators, respectively; for second and third order the potential is determined by solutions to Painlevé IV (PIV) and Painlevé V (PV) equations. Taking advantage of this connection, later on we will find solutions to PIV and PV equations expressed in terms of confluent hypergeometric functions. Furthermore, we will classify them into several solution hierarchies, according to the specific special functions they are connected with.
Authors:
;  [1]
  1. Departamento de Física, Cinvestav, A.P. 14-740, 07000 México D.F. (Mexico)
Publication Date:
OSTI Identifier:
22264084
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1575; Journal Issue: 1; Conference: Latin-American school of physics Marcos Moshinsky Elaf: Nonlinear dynamics in Hamiltonian systems, Mexico City (Mexico), 22 Jul - 2 Aug 2013; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; EQUATIONS; HYPERGEOMETRIC FUNCTIONS; MATHEMATICAL SOLUTIONS; OSCILLATORS; POLYNOMIALS; POTENTIALS; QUANTUM MECHANICS; SUPERSYMMETRY