Abstract:

In agreement with recent results of GellMann and Hartle, we approximate electron motions in ground state Li7H1 and Li7H2 using an energy conserving numerical method for the solution of Newton's equations and a novel assumption about the interaction of the bonding electrons. Initial calculations for the first excited state of Li7H1 are also discussed.
I. Introduction. Quantum dynamics is usually perceived through the time dependent Schrödinger equation, for which related analytical and computational problems appear to be insurmountable at the present time. There is however an alternate approach which can be implemented readily when the dynamical behavior is periodic. This approach is through the quantum dynamical Ehrenfest equations, which are Newtonian dynamical equations for expectation values (1,2). Moreover, when the wave function is narrow, Newton's equations themselves provide dynamical approximations over short time periods(3,4). Hence, energy conserving numerical methodology applied to Newton's equations over only a few time periods could characterize correct results over long times for phenomena which are periodic. It is this approach we will implement in the present paper and will apply it first to the hydride Li7H1 in ground state. The methodology developed will then be extended to Li7H2. Electron motions are shown graphically and are consistent with Heisenberg uncertainty because the numerical calculations are coarse in the sense of GellMann and Hartle (4). We also report on initial calculations for the first excited state of Li7H1. 