Superposition and Geometry for Evidence and Quantum Mechanics in the Tensor Calculus

Introduction

In this chapter we prove that the interference in Coherent Quantum Mechanics is represented by a deformed space of the intensity for different particle beams. In the interference the complex number representation of the quantum mechanics is substituted by general real coordinates where the angles between general coordinates are the difference of the phases. To reformulate the traditional quantum model, we use the evidence theory and its geometric image. The evidence theory defines a non additive probability denoted basic probability assignment. We assume that in quantum mechanics for interference and entanglement phenomena, the probability is not the traditional probability but is the basic probability assignment in the evidence theory.