Journal of Modern Physics, 2012, 3, 312-333 doi:10.4236/jmp.2012.34044 Published Online April 2012 (http://www.SciRP.org/journal/jmp) An Introductory Study of the Hydrogen Atom with Paraquantum Logic João Inácio Da Silva Filho 1,2 1 Group of Applied Paraconsistent Logic, Santa Cecília University, Santos, Brazil 2 Institute for Advanced Studies, University of São Paulo Cidade Universitária, São Paulo, Brazil Email: inacio@unisanta.br Received January 3, 2012; revised February 28, 2012; accepted March 12, 2012 ABSTRACT Paraquantum Logics (P QL ) has its origins in the fundamental concepts of the Paraconsistent Annotated Logics (PAL) whose main feature is to be capable of treating contradictory information. Based on a class of logics called Paraconsis- tent Logics with annotations of two values (PAL2v), P QL performs a logical treatment on signals obtained by meas- urements on physical quantities which are considered Observable Variables in the physical world. In the process of ap- plication of the P QL the obtained values are transformed in Evidence Degrees and represented on a Lattice of four Ver- tices where special equations transform these degrees into Paraquantum logical states ψ which propagate. The propaga- tion of Paraquantum logical states provides us with results which can be interpreted and modeled through phenomena studied in physics. Using the paraquantum equations, we investigate the effects of balancing of Energies and the quan- tization and transience properties of the Paraquantum Logical Model in real Physical Systems. As a demonstration of the usage of the paraquantum equations we perform a numerical comparative study that applies the P QL to the Bohr’s model to find the energy levels of the Hydrogen atom. It is verified that the values of energy in each level of the Paraq- uantum logical model of the Hydrogen atom are close to the values found by the conventional way. The results through the Paraquantum Logic allow considering other important properties of the atom, as the forecast of number of electrons in each layer. Keywords: Paraconsistent Logic; Paraquantum Logic; Classical Physic; Relativity Theory; Quantum Mechanics 1. Introduction The conception of physical system models that prove to be more efficient in order to respond to the analyses in extreme conditions becomes necessary when we verify inconsistencies in computation obtained from models which reproduce the same natural phenomenon but are from different areas of physics (see [1,2]). In order to create a mathematical tool that conveniently make these results compatible, we present in this paper a model based on the concepts of a non-Classical logics called Paraconsistent Logics (PL) (see [3,4]). A Paraconsistent Logic is a non-classical logic which revokes the principle of non-Contradiction and admits the treatment of contradictory information in its theoreti- cal structure (see [4,5]). The foundational principles of the Paraconsistent Logics can be seen with details in [1] and [4]. In [5] we presented an interpretation of the Paraconsistent Logic that it resulted in the foundations of an applicable model in physical systems. This extension of the PL was denominated of Paraconsistent Annotated Logic with annotation of two values (PAL2v). The PAL2v is a class of Paraconsistent Logics particularly represented through a Lattice of four vertices and from its foundations the Paraquantum Logics (P QL ) was cre- ated. The organization of the paper is as follows: in the Sec- tion 2 the basic concepts, the interpretation and the main equations of the LPA2v Logic are presented. In Section 3 the main concepts of the Paraquantum Logic are pre- sented. In the Section 4 a Paraquantum Logical Model is proposed to quantization of values of Physical Quantities. In Section 5 the Paraquantum Logical Model is applied for calculations of the Energy levels in the Hydrogen Atom. In the Section 6 are presented conclusions about the Paraquantum Logic application results in the Hydro- gen Atom. 2. The Main Concepts of the Paraconsistent Annotated Logic with Annotation of Two Values (PAL2v) According to [5] we can obtain through the PAL2v a representation of how the annotations or evidences ex- press the knowledge about a certain proposition P. This is done through a lattice on the real plane with pairs (, Ȝ) Copyright © 2012 SciRes. JMP