A Note on Shape Invariant Potentials for Discretized Hamiltonians
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 dis...
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| creator | Sonnenschein, Jonas Tsulaia, Mirian |
| description | 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. |
| doi_str_mv | 10.48550/arxiv.2205.10100 |
| format | Article |
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| subjects | Coulomb potential Discretization Energy spectra Hamiltonian functions Mechanical systems Physics - High Energy Physics - Theory Physics - Quantum Physics Quantum mechanics Quantum physics Supersymmetry Wave functions |
| title | A Note on Shape Invariant Potentials for Discretized Hamiltonians |
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