scholarly journals Application of the Shannon Entropy in the Construction of a Paraconsistent Model of the Atom

2019 ◽  
Author(s):  
João Inácio da Silva Filho
Keyword(s):  
Shannon Entropy ◽  
Energy Levels ◽  
Paraconsistent Logic ◽  
Main Property ◽  
Mineral Oil ◽  
Wave Functions ◽  
Logarithmic Function ◽  
Planck Constant ◽  
Quality Detection ◽  
Annotated Logic

In this work, we present a model of the atom that is based on nonclassical logic called paraconsistent logic (PL), which has the main property of accepting the contradiction in logical interpretations without the conclusions being annulled. The model proposed in this work is constructed with the extension of PL called paraconsistent annotated logic with annotation of two values (PAL2v) that is associated with an interlaced bilattice of four vertices. We used the logarithmic function of the Shannon entropy H(s) with the inclusion of the normalized Planck constant ħ to construct the paraconsistent equations. Through the analyses of the interlaced bilattice, comparative values are obtained for some of the phenomena and effects of quantum mechanics, such as superposition of states, quantum entanglement, wave functions, and equations that determine the energy levels of the layers of the atom. At the end of this article, we use the hydrogen atom as the basis of the representation of the PAL2v model, where the values of the energy levels in six orbital layers are obtained. As an example, we present a possible method of applying the PAL2v model to the use of Raman spectroscopy signals in quality detection of lubricating mineral oil.

scholarly journals Application of Shannon Entropy in the Construction of a Paraconsistent Model of the Atom

2020 ◽  
Author(s):  
João Inácio da Silva Filho
Keyword(s):  
Shannon Entropy ◽  
Quantum Physics ◽  
Energy Levels ◽  
Oil Quality ◽  
Paraconsistent Logic ◽  
Main Property ◽  
Wave Functions ◽  
Logarithmic Function ◽  
Proposed Model ◽  
Annotated Logic

In this work, we present a model of the atom that is based on a nonclassical logic called paraconsistent logic (PL), which has the main property of accepting the contradiction in logical interpretations without the conclusions being annulled. The proposed model is constructed with an extension of PL called paraconsistent annotated logic with annotation of two values (PAL2v), which is associated with an interlaced bilattice of four vertices. We use the logarithmic function of the Shannon entropy H(s) to construct the paraconsistent equations and thus adapt a probabilistic model for representations in quantum physics. Through analyses of the interlaced bilattice, comparative values are obtained for some of the phenomena and effects of quantum mechanics, such as superposition of states, quantum entanglement, wave functions, and equations that determine the energy levels of the layers of an atom. At the end of this article, we use the hydrogen atom as a basis of the representation of the PAL2v model, where the values of the energy levels in six orbital layers are obtained. As an example, we present a possible method of applying the PAL2v model to the use of Raman spectroscopy signals in the detection of lubricating mineral oil quality.

scholarly journals Application of Shannon Entropy in the Construction of a Paraconsistent Model of the Atom

2020 ◽  
Vol 18 ◽  
pp. 78-113
Author(s):  
João Inácio da Silva Filho
Keyword(s):  
Shannon Entropy ◽  
Quantum Physics ◽  
Energy Levels ◽  
Oil Quality ◽  
Paraconsistent Logic ◽  
Main Property ◽  
Wave Functions ◽  
Logarithmic Function ◽  
Proposed Model ◽  
Annotated Logic

In this paper, we present a model of the atom that is based on a nonclassical logic called paraconsistent logic (PL), which has the main property of accepting the contradiction in logical interpretations without the conclusions being annulled. The proposed model is constructed with an extension of PL called paraconsistent annotated logic with annotation of two values (PAL2v), which is associated with an interlaced lattice of four vertices. We use the logarithmic function of the Shannon entropy H(s) to construct the paraconsistent equations and thus adopt a probabilistic model for representations in quantum physics. Through analyses of the interlaced lattice, comparative values are obtained for some of the phenomena and effects of quantum mechanics, such as superposition of states, wave functions, and equations that determine the energy levels of the atomic shells of an atom. At the end of this article, we use the hydrogen atom as a basis for the representation of the PAL2v model, where the values of the energy levels in six orbital shells are obtained. As an example, we present a possible method of applying the PAL2v model to the use of Raman spectroscopy signals in the detection of lubricating mineral oil quality.

scholarly journals Intercombination Transitions between Levels X1Σg+ and A 3Πu in C2

1987 ◽  
Vol 120 ◽  
pp. 103-105
Author(s):  
J. Le Bourlot ◽  
E. Roueff
Keyword(s):  
Transition Probabilities ◽  
Energy Levels ◽  
Wave Functions ◽  
Spin Orbit Coupling ◽  
Energy Matrix ◽  
First Order ◽  
Emission Transition ◽  
Intercombination Transition ◽  
The One ◽  
Potential Curves

We present a new calculation of intercombination transition probabilities between levels X1Σg+ and a 3Πu of the C2 molecule. Starting from experimental energy levels, we calculate RKR potential curves using Leroy's Near Dissociation Expansion (NDE) method; these curves give us wave functions for all levels of interest. We then compute the energy matrix for the four lowest states of C2, taking into account Spin-Orbit coupling between a 3Πu and A 1Πu on the one hand and X 1Σ+g and b 3Σg− on the other. First order wave functions are then derived by diagonalization. Einstein emission transition probabilities of the Intercombination lines are finally obtained.

Relativistic quantum bouncing particles in a homogeneous gravitational field

2021 ◽  
pp. 2150098
Author(s):  
Ar Rohim ◽  
Kazushige Ueda ◽  
Kazuhiro Yamamoto ◽  
Shih-Yuin Lin
Keyword(s):  
Gravitational Field ◽  
Relativistic Effect ◽  
Relativistic Quantum ◽  
Energy Levels ◽  
Nonrelativistic Limit ◽  
Wave Functions ◽  
Dirac Equations ◽  
Rindler Coordinates ◽  
Klein Gordon ◽  
Homogeneous Gravitational Field

In this paper, we study the relativistic effect on the wave functions for a bouncing particle in a gravitational field. Motivated by the equivalence principle, we investigate the Klein–Gordon and Dirac equations in Rindler coordinates with the boundary conditions mimicking a uniformly accelerated mirror in Minkowski space. In the nonrelativistic limit, all these models in the comoving frame reduce to the familiar eigenvalue problem for the Schrödinger equation with a fixed floor in a linear gravitational potential, as expected. We find that the transition frequency between two energy levels of a bouncing Dirac particle is greater than the counterpart of a Klein–Gordon particle, while both are greater than their nonrelativistic limit. The different corrections to eigen-energies of particles of different nature are associated with the different behaviors of their wave functions around the mirror boundary.

A study of the compactness of wave functions based on Shannon entropy indices: a seniority number approach

2015 ◽  
pp. 115-121
Author(s):  
Luis Lain ◽  
Alicia Torre ◽  
Diego R. Alcoba ◽  
Ofelia B. Oña ◽  
Gustavo E. Massaccesi
Keyword(s):  
Shannon Entropy ◽  
Wave Functions ◽  
Seniority Number

Semi-empirical Molecular Orbital Energy Levels of the Hexammine and Chloroammine Complexes of Co(IV)

1967 ◽  
Vol 22 (2) ◽  
pp. 170-175 ◽  
Author(s):  
Walter A. Yeranos ◽  
David A. Hasman
Keyword(s):  
Molecular Orbital ◽  
Energy Levels ◽  
Empirical Evaluation ◽  
Wave Functions ◽  
Electronic Transitions ◽  
Orbital Energy ◽  
Molecular Orbital Energy ◽  
The One ◽  
Semi Empirical

Using the recently proposed reciprocal mean for the semi-empirical evaluation of resonance integrals, as well as approximate SCF wave functions for Co3+, the one-electron molecular energy levels of Co (NH3) 3+, Co (NH3) 5Cl2+, and Co (NH3) 4Cl21+ have been redetermined within the WOLFSBERG–HELMHOLZ approximation. The outcome of the study fits remarkably well with the observed electronic transitions in the u.v. spectra of these complexes and prompts different band assignments than previously suggested.

scholarly journals Spin-0 system of DKP equation in the background of a flat class of Gödel-type spacetime

2019 ◽  
Vol 35 (07) ◽  
pp. 2050031 ◽  
Author(s):  
Faizuddin Ahmed ◽  
Hassan Hassanabadi
Keyword(s):  
Energy Levels ◽  
Wave Functions ◽  
Dkp Equation ◽  
Free Particles ◽  
The Individual

In this paper, we investigate the Duffin–Kemmer–Petiau (DKP) equation for spin-0 system of charge-free particles in the background of a flat class of Gödel-type spacetimes, and evaluate the individual energy levels and corresponding wave functions in detail.

A new iterative method for calculating energy levels and wave functions

2000 ◽  
Vol 112 (20) ◽  
pp. 8765-8771 ◽  
Author(s):  
Shi-Wei Huang ◽  
Tucker Carrington
Keyword(s):  
Iterative Method ◽  
Energy Levels ◽  
Wave Functions ◽  
New Iterative Method
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