New research based on the new high-order generalized uncertainty principle for Klein–Gordon equation

Abstract

A new high-order generalized uncertainty principle is proposed in this paper, which can modify the coordinate operator and the momentum operator simultaneously. Afterwards, the Klein–Gordon equation with linear scalar and vector potential is investigated in the context of new principle and whose corresponding exact analytical solutions are further derived. In addition, the above results are also verified in a pure algebraic fashion by using the property of shape invariance symmetry. Moreover, the influence of the minimum length parameter β on the energy spectrum of the Klein–Gordon equation is also discussed in detail in this article.