The quantum mechanical theory of environmental effects

Abstract

A basic postulate of wave mechanics is that the wave function of a microscopic system develops in time according to the equation iℏ∂ψ/∂ t = H ψ, where H , the Hamiltonian, is an operator which in general depends upon the time. If, and only if, the Hamiltonian is time-independent, then the solutions of this equation take the form ψ( q, t ) = ∑ n c n Ѱ n ( q )e -1 E n t /ℏ , (2) where the individual terms Ѱ n ( q ) are functions of the co-ordinates alone and the E n are the corresponding eigenvalues of the Hamiltonian, satisfying HѰ n = E n Ѱ n . (3)