istanaro!Hidden Supersymmetry of Electrostatic Fields: https://arxiv.org/abs/2209.01248
Juan D. García-Muñoz, A Raya
A hidden supersymmetry of electrostatic fields is evidenced. 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, through the appropriate choice of a charge density, to find the ground state of the corresponding supersymmetric initial potential. Furthermore, the associated electrostatic field profile of a Schr{ö}dinger-like solvable potentials can be determined