论文标题
经典静电场的超对称量子电位类似物
Supersymmetric Quantum Potentials Analogs of Classical Electrostatic Fields
论文作者
论文摘要
经典的静电场与施罗丁样的哈密顿量之间的关系已证明。因此，可以构建类似于经典静电场的超对称量子电位。提出将静电电势作为无节状函数的自然对数的ANSATZ，因此证明静电场满足了与二阶汇合超对称转换相关的Bernoulli方程。通过使用所谓的汇合算法，给定电荷密度，可以找到相应的静电场以及超对称电位。此外，可以确定相关的电荷密度和类似Schrödinger的可溶剂电位的静电场曲线。
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.
