Exact Solution of Dirac Equation with Charged Harmonic Oscillator in Electric Field: Bound States

TL;DR

This paper derives exact solutions for the Dirac equation with a charged harmonic oscillator in an electric field, providing analytic energy spectra and wavefunctions, and explores the nonrelativistic limit for quantum chemical applications.

Contribution

It presents the first exact solutions of the Dirac equation for a charged harmonic oscillator in an electric field using the NU method, including energy spectra and wavefunctions.

Findings

Exact s-wave solutions obtained for the Dirac equation with the potential model.

Analytic expressions for energy spectra and spinor wavefunctions derived.

Nonrelativistic limit matches and extends previous results.

Abstract

In some quantum chemical applications, the potential models are linear combination of single exactly solvable potentials. This is the case equivalent of the Stark effect for a charged harmonic oscillator (HO) in a uniform electric field of specific strength (HO in an external dipole field). We obtain the exact s-wave solutions of the Dirac equation for some potential models which are linear combination of single exactly solvable potentials (ESPs). In the framework of the spin and pseudospin symmetric concept, we calculate the analytic energy spectrum and the corresponding two-component upper- and lower-spinors of the two Dirac particles by the Nikiforov-Uvarov (NU) method, in a closed form. The nonrelativistic limit of the solution is also studied and compared with the other works.