Supersymmetric Quantum Potentials Analogs of Classical Electrostatic Fields

• URL: http://arxiv.org/abs/2209.01248v4
• Date: Tue, 19 Sep 2023 17:45:10 GMT
• Title: Supersymmetric Quantum Potentials Analogs of Classical Electrostatic Fields
• Authors: Juan D. Garc\'ia-Mu\~noz and A Raya
• Abstract summary: A relation between classical electrostatic fields and Schr"odinger-like Hamiltonians is evidenced. Supersymmetric quantum potentials analogous to classical electrostatic fields can be constructed.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A relation between classical electrostatic fields and Schr\"odinger-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 Schr\"odinger-like solvable potentials can be determined.

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