On superintegrable symmetry-breaking potentials in N-dimensional Euclidean space
| Autor: | G.C. Williams, Willard Miller, George S. Pogosyan, Ernie G. Kalnins |
|---|---|
| Rok vydání: | 2002 |
| Předmět: |
Euclidean space
Mathematical analysis Separation of variables Closure (topology) General Physics and Astronomy Statistical and Nonlinear Physics Separable space law.invention Quadratic algebra law Homogeneous space Cartesian coordinate system Symmetry breaking Mathematical Physics Mathematical physics Mathematics |
| Zdroj: | Journal of Physics A: Mathematical and General. 35:4755-4773 |
| ISSN: | 0305-4470 |
| DOI: | 10.1088/0305-4470/35/22/308 |
| Popis: | We give a graphical prescription for obtaining and characterizing all separable coordinates for which the Schr?dinger equation admits separable solutions for one of the superintegrable potentials Here xn+1 is a distinguished Cartesian variable. The algebra of second-order symmetries of the resulting Schr?dinger equation is given and, for the first potential, the closure relations of the corresponding quadratic algebra. These potentials are particularly interesting because they occur in all dimensions n ? 1, the separation of variables problem is highly nontrivial for them, and many other potentials are limiting cases. |
| Databáze: | OpenAIRE |
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