The Three-Dimensional Relativistic Schroedinger Equation for the Three-Body Problem

James G. Gilson

A.K. Petrauskas, L.Yu. Sabalyauskas

H. Pierre Noyes, Edwin D. Jones

L. Fortunato, Tomohiro Oishi

A new convenient method to diagonalize the non-relativistic many-body Schroedinger equation with two-body central potentials is derived. It combines kinematic rotations (democracy transformations) and exact calculation of overlap integrals between bases with different sets of mass-scaled Jacobi coordinates, thereby allowing for a great simplification of this formidable problem. We validate our method by obtaining a perfect correspondence with the exactly solvable three-body ($N=3$) Calogero model in 1D.

V. S. Bhasin, H. Jacob, Asoke N. Mitra

CAIChang-Ying, RENZhong-Zhou, JUGuo-Xing

For an exponentially position-dependent mass, we obtain the exact solutions of the three-dimensional Schroedinger equation by using coordinate transformation method for the reference problems with Coulomb potential, Kratzer potential, and spherically square potential well of infinite depth, respectively. The explicit expressions for the energy eigenvalues and the corresponding eigenfunctions of the three systems are presented.