Abstract

Since the inception of quantum mechanics, the classical limit has been an area of unease. Explanations proposed on this matter include the usage of Plank's constant, the decoherence parameter of the master's equation, or the quantum potential of Bohm's theory. An equally obscure related topic is the mixing of classical and quantum quantities in the dynamical equations. In this thesis, the subject of classical-quantum mixing will be studied. A method will be explored which will demonstrate one of several candidate methods whereby mixing may be removed and replaced by fully quantum non-relativistic equations. Through use of the quantum potential concept and the Feynman path integral, state-dependent forms of the classical scalar and vector potentials will be derived by assuming the existence of separate component wave functions for the particle and potential. The specific wave component | e attributed to the potential, will hold the effects of an environment. The resulting equations are devoid of classical potentials and can therefore be considered as purely quantum--no mixing takes place. The standard classical potentials emerge from the state-dependent equations by a condition which will be referred to as state-dependence reduction (SDR). Through SDR, the semi-quantum and purely quantum equations are qualitatively and quantitatively equivalent. The new purely quantum equations will be used both to interpret gauge symmetry and to clarify the reasoning behind the Aharonov-Bohm effect. It will be argued that the freedom of gauge is related to the freedom to choose from many different and distinct environments which reproduce the same experimental outcome. Likewise, the AB-effect is understood through the environment from which the topological structure of the electromagnetic field is represented. Several aspects of the environment responsible for the effective potentials will be calculated numerically for well-known physical situations including one-dimensional scattering, two-dimensional double-slit setup, two-dimensional Aharonov-Bohm effect, and the two-dimensional Dirac equation. The proposal of using state-dependent potentials to replace the semi-quantum equation represents a consistent generalization and unification of the quantum and classical potentials, and may offer some experimental results yet untapped.