Representações e aspectos quânticos de sistemas não-comutativos

Abstract

This paper explores initially, in a intuitive form, some questions of non-commutativity in space well as the motivations for the study of non-commutative theories. Then be given an overight in some aspects of quantum theory non-commutative addressed in the plan. Following the basic rules of the non-commutative, see how to build states that saturate the uncertainty relations, i.e., get the least possible uncertainty in the observable in question, for a construction of non-commutative algebra of coordinates. In particular, following the search of states that saturate both relations Heisenberg uncertainty modied and show saturation of the Schrodinger's determinant for a given Gaussian state. Then, will be built the propagator for the free particle from the construction of noncommutative version of the plane wave, exploring the idea of average in coherent states. And also exploring the idea of the construction of wave packet in the non-commutative plane, get its evolved form using the path integral formalism, ending with the analysis of the Fourier's transform in non-commutative space. This paper analyzes the results and what can be done in a next project, with the tools presented.