The factorization method and particular solutions of the relativistic Schrödinger equation of [formula omitted]th order ( [formula omitted

Abstract

The Schrödinger equation in the relativistic configuration space for a relativistic function Ψ(r) has the form of an infinite-order linear differential equation with an inherent small parameter ϵ=1/c at the higher derivatives. In the formal limit c→∞ this equation degenerates to the standard nonrelativistic Schrödinger equation. To simplify the problem, we have considered the nth order differential equation ( n=4,6) which corresponds to a truncation of the higher order derivative contributions. The linear nth order differential operator can be expressed in a factorized form: H ̂ = H ̂ n/2… H ̂ 2 H ̂ 1 , where H ̂ i are differential operators of second order. Solving the differential equation of second order, H ̂ 1Ψ(r)=0 , we can obtain a particular solutions of the nth order equation.