Exactly solvable interaction Hamiltonian of a neutral massive spin-1/2 particle with an external electrical field from Darboux transformation

Abstract

We construct a Darboux transformation for the free Hamiltonian of the one-dimensional four-component Dirac equation which generates the interaction Hamiltonian of a spin-1/2 neutral massive particle with an external electrical field through its magnetic moment. We interpret this interaction as coherent Schwinger interaction and consider a possible application of this result. We also construct a chain of the Darboux—Crum transformations for the four-component Dirac equation and briefly discuss the structure of the Lyapunov functions for the problem of the interaction with the periodic potentials.

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