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arXiv · 2205.10100

A Note on Shape Invariant Potentials for Discretized Hamiltonians

Jonas Sonnenschein·Mirian Tsulaia
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Abstract

Using the method of the "exact discretization" of the Schr\"odinger equation, we propose a particular discretized version of the N=2 Supersymmetric Quantum Mechanics. After defining the corresponding shape invariance condition, we show that the energy spectra and wavefunctions for discretized Quantum Mechanical systems can be found using the technique of N=2 Supersymmetric Quantum Mechanics exactly the same way as it is done for their continuous counterparts. As a demonstration of the present method, we find the energy spectrum for a discretized Coulomb potential and its ground state wave function.

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Jonas Sonnenschein, Mirian Tsulaia. 2022-05-20. A Note on Shape Invariant Potentials for Discretized Hamiltonians. https://doi.org/10.1142/s021773232250153x

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