| Relativistic harmonic oscillator is one of the solvable basic models in quantum mechanics,and the related research has attracted the attention of many researchers.This paper conducts research on the harmonic oscillator model affected by the magnetic field under the non-commutative space and the rainbow gravitational cosmic string space-time,which specifically includes two parts:We studied the DKP harmonic oscillator with Aharonov-Bohm potential in non-commutative space and the generalized DKP harmonic oscillator with uniform magnetic field.The equations of the DKP harmonic oscillator and the generalized DKP harmonic oscillator in the non-commutative space are obtained by Bopp transformation,and we solved the energy level and wave function asymptotic solutions of the system by using the Bethe-Ansatz method.We discussed the energy levels and wave functions for both cases.It is shown that the non-commutative parameter θ and the frequency of the oscillator have an influence on the energy eigenvalues and wave functions of the system in both cases.The absolute value of the energy level of the DKP harmonic oscillator under the action of the AB potential decreases with the increase of the order of the polynomial asymptotic solution.For the generalized DKP harmonic oscillator subjected to the uniform magnetic field along the Z axis,the effect of the magnetic field action is offset by the non-commutative effect and the influence of the Coulomb type potential function parameters of the generalized DKP harmonic oscillator.Based on the rainbow gravity model,we studied the K-G harmonic oscillator and the generalized K-G harmonic oscillator in the cosmic string space-time.By considering the existence of a uniform magnetic field and AB potential,we solved the energy level and wave function asymptotic solutions of the K-G harmonic oscillator and the generalized K-G harmonic oscillator with the Bethe-Ansatz method.We selected two groups of rainbow functions,and discussed the influence of the parameters of the rainbow function,the Planck energy and the angle parameter α on the K-G harmonic oscillator and the generalized K-G harmonic oscillator when n=1. |
