A Note on Shape Invariant Potentials for Discretized Hamiltonians

• URL: http://arxiv.org/abs/2205.10100v2
• Date: Mon, 17 Oct 2022 14:07:22 GMT
• Title: A Note on Shape Invariant Potentials for Discretized Hamiltonians
• Authors: Jonas Sonnenschein and Mirian Tsulaia
• Abstract summary: 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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