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Shape invariant potentials in higher dimensions |
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| Authors: | R Sandhya S Sree Ranjani AK Kapoor |
| Institution: | 1. Department of Physics, Osmania University, Hyderabad, India;2. School of Physics, University of Hyderabad, Hyderabad, 500046, India;3. Faculty of Science and Technology, ICFAI foundation for Higher Education, (Declared as deemed-to-be University u/s 3 of the UGC Act 1956), Dontanapally, Hyderabad, 501203, India;4. Department of Physics, Shiv Nadar University, Village Chithera, Tehsil Dadri, Gautam Budh Nagar, UP, 203207, India;5. Department of Physics, BITS-Pilani Hyderabad Campus, Jawahar Nagar, Shameerpet Mandal, Hyderabad 500078, India1 |
| Abstract: | In this paper we investigate the shape invariance property of a potential in one dimension. We show that a simple ansatz allows us to reconstruct all the known shape invariant potentials in one dimension. This ansatz can be easily extended to arrive at a large class of new shape invariant potentials in arbitrary dimensions. A reformulation of the shape invariance property and possible generalizations are proposed. These may lead to an important extension of the shape invariance property to Hamiltonians that are related to standard potential problems via space time transformations, which are found useful in path integral formulation of quantum mechanics. |
| Keywords: | Shape invariance Exactly solvable model Rational potential Orthogonal polynomial Space time transformations QHJ formalism |
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