(1) Physics Department, The Harvard-Westlake School, 3700, Coldwater Canyon, Studio City, 91604, USA;(2) Department of Sciences, University of California, Los Angeles, Extension Program, 10995, Le Conte Avenue, Los Angeles, CA 90024, USA
Abstract:
A new quantum mechanical wave equation describing the dynamics of an extended electron is derived via Bohmian mechanics. The solution to this equation is found through a wave packet approach which establishes a direct correlation between a classical variable with a quantum variable describing the dynamics of the center of mass and the width of the electron wave packet. The approach presented in this paper gives a comparatively clearer picture than approaches using elaborative manipulation of infinite series of operators. It is shown that the new Schrödinger equation is free of any runaway solutions or any acausal responses.