Exact, zero-energy, square-integrable solutions of a model related to the Maxwell’s fish-eye problem |
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Authors: | Adam J Makowski |
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Institution: | Institute of Physics, Nicolaus Copernicus University, ul. Grudzia¸dzka 5, 87-100 Toruń, Poland |
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Abstract: | A model, which admits normalizable wave functions of the Schrödinger equation at the energy of E = 0, is exactly solved and the solutions are compared to the corresponding classical trajectories. The wave functions are proved to be square-integrable for discrete (quantized) values of the coupling constant of the used potential. We also show that our model is a specific version of the well-known Maxwell’s fish-eye. This is performed with the help of a suitably chosen conformal mapping. |
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Keywords: | Fish-eye model Zero-energy solutions Quantum-classical correspondence |
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