Classical Solutions of Schroedinger Equations and Nonstandard Analysis

Abstract

It is believed that classical mechanics is obtained from quantum mechanics by taking the limit of h —> 0. Such a consideration is easily understood in the following discussions: The Schroedinger equation is generally written down as

$$ih\frac{{\partial \Psi (r,t)}}{{\partial t}} = H\Psi (r,t)$$

(1)

where Hamiltonian is given by

$$H = (1/2m)[ - {(h\nabla )^2} + V(r)]$$