International Journal of Mathematics and Mathematical Sciences
Volume 3 (1980), Issue 2, Pages 351-368

Closed form bound-state perturbation theory

Ollie J. Rose1 and Carl G. Adler1

1SDC Integrated Services, Inc., Hampton, Virginia 23666, USA
2Physics Department, East Carolina University, Greenville, North Carolina 27834, USA

Received 23 January 1979; Revised 18 December 1979

Copyright © 1980 Ollie J. Rose and Carl G. Adler. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The perturbed Schrödinger eigenvalue problem for bound states is cast into integral form using Green's Functions. A systematic algorithm is developed and applied to the resulting equation giving rise to approximate solutions expressed as functions of the given perturbation parameter. As a by-product, convergence radii for the traditional Rayleigh-Schrödinger and Brillouin-Wigner perturbation theories emerge in a natural way.