INTERTWINING OF EXACTLY SOLVABLE DIRAC EQUATIONS WITH ONE-DIMENSIONAL POTENTIALS

The method of intertwining is used to construct transformations between one-dimensional electric potentials or one-dimensional external scalar fields for which the Dirac equation is exactly solvable. The transformations are analogous to the Darboux transformations between Schrodinger potentials. It is shown that a class of exactly solvable Dirac potentials corresponds to soliton solutions of the modified Korteweg-deVries (MKdV) equation, just as certain Schrodinger potentials are solitons of the Korteweg-deVries equation. It is also shown that the intertwining transformations are related to Backlund transformations for MKdV. The structure of the intertwining relations is shown to be described by an N = 4 superalgebra, generalizing supersymmetric quantum mechanics to the Dirac case.