Equations of change in configuration space

Abstract

AbstractThis paper is a summary of a detailed treatment, given elsewhere, in which (gauge invariant), equations of change (at points in configuration space) of arbitrary dynamical properties of an N‐particle quantum‐mechanical system in the presence (or absence) of an arbitrary (time‐ and space‐varying) classical electromagnetic field are derived for an arbitrary Hamiltonian by making use of both the Maxwell and the Schrödinger time‐dependent equations. The properties at a point in configuration space are defined so as to be closely related to observables and the forces are related to their classical counterparts. The rates of change of linear momentum and angular momentum are closely related to the classical Lorentz force and the Lorentz torque, respectively. The rate of change of energy is the work done on the system by E(t), the time‐dependent part of the external electromagnetic field. The reason for E(t) and its definition of the energy for a system in a time‐varying electromagnetic field is explained. The Breit‐Pauli Hamiltonian is required to treat “state‐to‐state” molecular problems and the detailed equations of change using this Hamiltonian are used as examples.