A Note on Shape Invariant Potentials for Discretized Hamiltonians
arXiv:2205.10100 · doi:10.1142/S021773232250153X
Abstract
Using the method of the "exact discretization" of the Schrödinger 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.
10 pages, LaTeX, References added