Supersymmetric Quantum Potentials Analogs of Classical Electrostatic Fields
arXiv:2209.01248 · doi:10.1142/S021988782450052X
Abstract
A relation between classical electrostatic fields and Schrödinger-like Hamiltonians is evidenced. Hence, supersymmetric quantum potentials analogous to classical electrostatic fields can be constructed. Proposing an ansatz for the electrostatic potential as the natural logarithm of a nodeless function, it is demonstrated that the electrostatic fields fulfil the Bernoulli equation associated to a second-order confluent supersymmetric transformation. By using the so-called confluent algorithm, it is possible, given a charge density, to find the corresponding electrostatic field as well as the supersymmetric potentials. Furthermore, the associated charge density and the electrostatic field profile of Schrödinger-like solvable potentials can be determined.
arXiv comment15 pages, 4 figures
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