Integration of the Heisenberg equations for inverse power-law potentials.

Abstract

The direct method of integration of the operator Heisenberg equations of motion is extended to the solution of quantum tunneling when the central potential is a sum of inverse powers of the radial distance. By obtaining the equation of motion for the Weyl-ordered basis set {l_brace}{ital S}{sub {ital m},{ital n}}({ital t}){r_brace} formed from {ital r}({ital t}) and {ital p}{sub {ital r}}({ital t}), one can express the time evolution of any member of the set as an infinite sum involving the operators {l_brace}{ital S}{sub {ital m},{ital n}}(0){r_brace}. The direct integration enables one to find the expectation values of the radial position operator and its conjugate momentum and higher moments of these operators as functions of time. {copyright} {ital 1996 The American Physical Society.}