Supersymmetric quantum mechanics for two-dimensional disk |
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Authors: | Akira Suzuki Ranabir Dutt Rajat K Bhaduri |
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Institution: | (1) Department of Physics, Tokyo University of Science, 162-8601 Tokyo, Japan;(2) Department of Physics, Visva Bharati University, 731 235 Santiniketan, India;(3) Department of Physics and Astronomy, McMaster University, L9H 6T6 Hamilton, Canada |
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Abstract: | The infinite square well potential in one dimension has a smooth supersymmetric partner potential which is shape invariant.
In this paper, we study the generalization of this to two dimensions by constructing the supersymmetric partner of the disk
billiard. We find that the property of shape invariance is lost in this case. Nevertheless, the WKB results are significantly
improved when SWKB calculations are performed with the square of the superpotential. We also study the effect of inserting
a singular flux line through the center of the disk. |
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Keywords: | Supersymmetric quantum mechanics SWKB disk billiard flux lines |
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