Exact solution of generalized Dirac oscillator in electric field

We study generalized (1+1)-dimensional Dirac oscillator in nonuniform electric field. It is shown that in the case of specially chosen electric field the eigenvalue equation can be casted in the form of supersymmetric quantum mechanics. It gives a possibility to find exact solution for the energy spectrum of the generalized Dirac oscillator in nonuniform electric field. Explicit examples of exact solutions are presented. We show that sufficiently large electric field destroys the bounded eigenstates.