A Quantum Mechanics Picture

TL;DR

This paper introduces a new quantum mechanics representation based on position, momentum, and energy eigenvalues, providing a trajectory-based perspective that complements traditional wave function approaches.

Contribution

It presents a wave function-independent set of equations relating observables, introducing the concept of quantum force and a novel particle description using auxiliary wave particles.

Findings

Derivation of equations independent of wave functions

Introduction of quantum force from potential and momentum

Proposal of wave particles to describe probabilistic quantum behavior

Abstract

A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables. In this view, a particle has a known trajectory and at any point on space there is a linear momentum associated. Trajectory here, can be viewed as if a measurement were taken continuously. This picture does not change current quantum mechanics interpretation, rather it comes as a new route of calculation. Also, wave function can be retrieved performing an integration in all space for linear momentum. Equations derived in this work, present a potential dependent on linear momentum originating what we call quantum force. A particle experiences a total force whose resultant is composed by classic and quantum force, evolving on time according to it. In terms of evaluation, a single particle could be described by a set of auxiliary particles named as wave particles(WP). They will start with a range of initial conditions and will collectively describe probabilistic aspects of quantum mechanics. We expect this route could be applied to many problems, such as multi-body systems.