Abstract
In this work we presented a study of the obtaining of the spectral line emissions of the hydrogen atom using equations that are originated from the foundations of the Paraquantum Logic (PQL). Based on a class of logics called Paraconsistent Logics with annotation of two values (PAL2v), PQL performs a logical treatment on signals obtained by measurements on physical quantities which are considered Observable Variables in the physical world. In the process of application of the PQL the obtained values are transformed in Evidence Degrees and represented on a Lattice of four Vertices where special equations transform these degrees into Paraquantum logical states ψ which propagate. This allows creating Paraquantum logical models of physical systems of the real world. Using the paraquantum equations, we investigated the hydrogen atom spectrum and his main series known. We performed a numerical comparative study that applies the Paraquantum Logical Model to calculate the wavelengths values. The values of wavelengths obtained by the Paraquantum Equations are compared by the results found by the Rydberg formula and are verified that the series of the spectral line emissions of the hydrogen atom can be identified with the representative Lattices of the Paraquantum Logic. Through the application of the Paraquantum equations it was found a numeric value relates the layers of Paraquantum model of the Hydrogen atom. This value represents a constant that relates the Lattices that compose the Paraquantum universe, and it was denominated Paraquantum Structure Constant, whose symbol is αψ. The obtained results of the comparison demonstrate that the Paraquantum Logic comes with good possibilities of being the ideal logic to model our physical reality.
Highlights
IntroductionA Paraconsistent Logic is a non-classical logic which revokes the principle of non-Contradiction and admits the treatment of contradictory information in its theoretical structure [1,2]
A Paraconsistent Logic is a non-classical logic which revokes the principle of non-Contradiction and admits the treatment of contradictory information in its theoretical structure [1,2].The real applications of the Paraconsistent Logic (PL) in programming of computation systems began with an interpretative form that it used annotations, and, for that reason, the PL passed to be denominated of Paraconsistent Annotated Logic (PAL)
The values of wavelengths obtained by the Paraquantum Equations are compared by the results found by the Rydberg formula and are verified that the series of the spectral line emissions of the hydrogen atom can be identified with the representative Lattices of the Paraquantum Logic
Summary
A Paraconsistent Logic is a non-classical logic which revokes the principle of non-Contradiction and admits the treatment of contradictory information in its theoretical structure [1,2]. From all four vertices, we have the following interpretation: PI = P(0.5, 0.5) → The annotation ( , ) = (0.5, 0.5) assigns intuitive reading that P is undefined. As it can be seen in the study of the PAL presented in [5] with the values of x and y that vary between 0 and 1 and being considered in an Unitary Square on the Cartesian Plane (USCP), we can get linear transformations for a Lattice k of analogous values to the associated Lattice τ of the PAL2v. The second coordinate of the transformation (1) is called Contradiction Degree Dct. So, the Contradiction Degree is obtained by: Dct + 1.
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