Six-dimensional flow and the three-dimensional Schroedinger equation

Sergei N Vlasov, L. V. Piskunova, V. I. Talanov

A. O. Barut

The 15-parameter nonrelativistic limit of the conformal group and its linear realization in the six-dimensional space are determined. It is shown that the massive free Schroedinger equation is invariant under a 15-parameter set of transformations enlarging the 12-parameter Schroedinger group. It is shown how this set arises from the conformal group, and the quantum-mechanica1 representation of the generators is determined. (auth)

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.

John D. McGervey