THE MATHEMATICAL BASIS FOR DETERMINISTIC QUANTUM MECHANICS AND APPLICATION TO HARMONIC OSCILLATORS

Abstract

The concept of deterministic theory underlying quantum mechanics, usually referred to as “hidden variable theoriesâ€. For instance, one may or may not assume the occurence of information loss at tiny distance scales. One may suspect some sort of cellular automaton or a classical system of continuous fields, or even classical loops, D-branes, or whatever. We discuss Gerardus ‘t Hooft idea that refer to as  pre-quantization, where the physical system is not modified and complex systems are handled  probabilistically. Our results for harmonic oscillators indicate that the energy eigenstates of a quantum system are going to be nice. The next one urgent question must be answered is how to construct explicit models in which energy can be seen extrinsic and how can we find its limit cycles. An atractive related problem that found by us is how to introduce weak interactions between two nearly independent systems.