Hamiltonians with two-ladder spectra and solutions to the Painlevé IV equation

8th International Symposium on Quantum Theory and Symmetries

Bermudez, David^1,2 ; Fernández C, David J.^1

Departamento de Física, Cinvestav, AP 14-740, 07000 Mexico DF, Mexico^1

Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel^2

关键词: Complex solution;    Harmonic oscillators;    Heisenberg algebras;    I-V equation;    Painleve;    Second-order polynomial;    Third order;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/512/1/012017/pdf
DOI  :  10.1088/1742-6596/512/1/012017

来源: IOP

【 摘 要 】

Some supersymmetric partners of the harmonic oscillator Hamiltonian possess third-order differential ladder operators and, thus, they realize the second-order polynomial Heisenberg algebras. The corresponding spectra consist of an infinite ladder of energy levels plus a finite one that can be placed at any position with respect to the infinite ladder. Both of them have equally spaced energy levels. Departing from these Hamiltonians several families of real and complex solutions to the Painleve´ IV equation with real parameters will be generated.