Relativistic oscillators in new type of the extended uncertainty principle

Abstract

We present the exact solutions of one-dimensional Klein–Gordon and Dirac oscillators subject to the uniform electric field in the context of the new type of the extended uncertainty principle using the displacement operator method. The energy eigenvalues and eigenfunctions are determined for both cases. For the Klein–Gordon oscillator case, the wave functions are expressed in terms of the associated Laguerre polynomials and for the Dirac oscillator case, the wave functions are obtained in terms of the confluent Heun functions. The limiting cases are also studied using the special values of the physical parameters.