The factorization method and particular solutions of the relativistic Schrodinger equation of nth order (n=4, 6)

The Schrodinger equation in the relativistic configuration space for a rela tivistic function psi(r) has the form of an infinite-order linear different ial equation with an inherent small parameter epsilon = Ile at the higher d erivatives. In the formal Limit c --> infinity this equation degenerates to the standard nonrelativistic Schrodinger equation. To simplify the problem, we have considered the nth order differential equa tion (n = 4, 6) which corresponds to a truncation of the higher order deriv ative contributions. The Linear nth order differential operator can be expr essed in a factorized form: (H) over cap = (H) over cap(n/2) ... (H) over c ap(2) (H) over cap (H) over cap(1), where (H) over cap(i) are differential operators of second order. Solving the differential equation of second orde r, (H) over cap(1)psi(r) = 0, we can obtain a particular solutions of the n th order equation. (C) 2000 Elsevier Science B.V. All rights reserved.