Supersymmetric quantum mechanics and Painlevé equations
- Departamento de Física, Cinvestav, A.P. 14-740, 07000 México D.F. (Mexico)
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.
- OSTI ID:
- 22264084
- Journal Information:
- AIP Conference Proceedings, Vol. 1575, 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); ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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