QUASI-CLASSICAL MODEL FOR ONE-DIMENSIONAL POTENTIAL WELL

Abstract

Particle in one dimensional potential well demonstrates typical quantum mechanical behaviors determined by the related Schrodinger equation. The problem is solved here with a quasi-classical particle model that qualifies for quantum wave description. Our results cover majority of previous conclusions and reveal new mechanisms that, closure of the particle’s trajectory leads to quantization and lateral projections of particle’s three dimensional trajectories generate the Schrodinger wave functions for different energies. We explain that, Schrodinger wave functions represent different modes of particle’s motion and their amplitudes might measure the probability density that the particle is to be observed, but their interference invalids the probabilistic implication.