Superintegrability with third order integrals of motion, cubic algebras, and supersymmetric quantum mechanics. I. Rational function potentials

被引:61
作者
Marquette, Ian [1 ,2 ]
机构
[1] Univ Montreal, Dept Phys, Montreal, PQ H3C 3J7, Canada
[2] Univ Montreal, Ctr Rech Math, Montreal, PQ H3C 3J7, Canada
关键词
algebra; rational functions; supersymmetric quantum mechanics; SINGULAR POTENTIALS; DEFORMED OSCILLATOR; SYSTEMS; HAMILTONIANS; SYMMETRY; EQUATION; FACTORIZATION; DIMENSIONS;
D O I
10.1063/1.3013804
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We consider a superintegrable Hamiltonian system in a two-dimensional space with a scalar potential that allows one quadratic and one cubic integrals of motion. We construct the most general cubic algebra and we present specific realizations. We use them to calculate the energy spectrum. All classical and quantum superintegrable potentials separable in Cartesian coordinates with a third order integral are known. The general formalism is applied to quantum reducible and irreducible rational potentials separable in Cartesian coordinates in E-2. We also discuss these potentials from the point of view of supersymmetric and PT-symmetric quantum mechanics.
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页数:23
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