Relation between Green’s functions for different potentials

Saifuddin

The recurrence relations between Green functions are derived for the two and three particle potentials. The time variation of the field operator is used for the derivation of these recurrence relatiions.

S�ren Berg Padkj�r, Esper Dalgaard

Robert A. Mapleton

In a recent paper by this author, the singular wave function matrix of Mo/ller was used to obtain the scattering solution for the nonrelativistic Coulomb operator. In the present paper this singular wave function operator is defined differently. This definition is deduced from the relation of the characteristic form of the Green's function to the branch cut in the continuous part of the spectrum of the Green's function. As a consequence of this interpretation, the calculation difficulties of the previous paper do not occur. This method is also used to obtain the scattering solution for the attractive square-well potential.

Z. A. Kasamanyan

Colin John Lambert

Axel Schulze‐Halberg

We obtain a new relation between Green's functions of the time-dependent Schrödinger equation for stationary potentials and Green's functions of the same equation for certain time-dependent potentials. The relation obtained here emerges very easily from a transformation introduced by Ray [J.R. Ray, Phys. Rev. A26 (1982) 729] and generalizes former work of Dodonov, et al. [V.V. Dodonov, V.I. Man'ko, and D.E. Nikonov, Phys. Lett. A162 (1992) 359.]