scholarly journals The application bispherical coordinate in Schrödinger equation for Mobius square plus modified Yukawa potential using Nikiforov Uvarov Functional Analysis (NUFA) method

2020 ◽  
Vol 4 (2) ◽  
pp. 48
Author(s):  
Briant Sabathino Harya Wibawa ◽  
A Suparmi ◽  
C Cari
Keyword(s):  
Functional Analysis ◽  
Wave Function ◽  
Energy Spectrum ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Yukawa Potential ◽  
Radial Part ◽  
Angular Part ◽  
Variable Separation Method ◽  
Bispherical Coordinates

<p class="Abstract">The application bispherical coordinates in Schrödinger equation for the Mobius square plus modified Yukawa potential have been obtained. The Schrödinger equation in bispherical coordinates for the separable Mobius square plus modified Yukawa potential consisting of the radial part and the angular part for the Mobius square plus modified Yukawa potential is solved using the variable separation method to reduce it to the radial part and angular part Schrödinger equation. The aim of this study was to solve the Schrödinger's equation of radial in bispherical coordinates for the Mobius square plus modified Yukawa potential using the Nikiforov Uvarov Functional Analysis (NUFA) method. Nikiforov Uvarov Functional Analysis (NUFA) method used to obtained energy spectrum equation and wave function for the Mobius square plus modified Yukawa potential. The result of energy spectrum equation for Mobius square plus modified Yukawa potential can be shown in Equation (50). The result of un-normalized wave function equation for Mobius square plus modified Yukawa potential can be shown in Table 1.</p>

scholarly journals ANALYTICAL SOLUTION OF SCHRÖDINGER EQUATION IN BISPHERICAL COORDINATE FOR MOBIUS SQUARE PLUS MODIFIED YUKAWA POTENTIAL USING NIKIFOROV UVAROV FUNCTIONAL ANALYSIS (NUFA) METHOD WITH ITS THERMODYNAMICS PROPERTIES FOR DIATOMIC MOLECULES

2021 ◽  
Vol 17 (37) ◽  
pp. 111-134
Author(s):  
Briant Sabathino Harya WIBAWA ◽  
A SUPARMI ◽  
C CARI
Keyword(s):  
Functional Analysis ◽  
Wave Function ◽  
Partition Function ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Diatomic Molecules ◽  
Radial Part ◽  
Radial Wave ◽  
Vibrational Partition Function ◽  
Bispherical Coordinates

Background: The analytical solution of the Schrödinger equation in bispherical coordinates has attracted a great deal of interest for theoretical physics researchers in the branch of quantum physics. The energy and wave function are solutions of the Schrödinger equation which are very important because it contains all necessary information regarding the behavior of quantum systems. Aim: This study aimed to obtain energy, radial wave functions and thermodynamic properties for diatomic molecules from the radial part of the Schrödinger equation in bispherical coordinates for the modified Mobius square plus Yukawa potential using the Nikiforov Uvarov Functional Analysis (NUFA) method. Methods: The variable separation method was applied to reduce the Schrodinger equation in bispherical coordinates to the radial part and angular part Schrodinger equation. The Schrodinger equation of the radial part in bispherical coordinates was solved using the Nikiforov Uvarov Functional Analysis (NUFA) method to obtain the energy equation and radial wave function. Furthermore, the vibrational partition function 𝑍 was obtained from the energy equation. The vibrational mean energy 𝑈, vibrational specific heat 𝐶, vibrational free energy 𝐹, and vibrational entropy 𝑆 were obtained from the vibrational partition function 𝑍. Results and Discussion: The results showed that the increase of parameters of 𝑛 and 𝛼 caused the decrease of energy, but the increase of parameters of 𝐿 and 𝑚0 caused the increase of energy. The radial quantum number 𝑛 and the potential range 𝛼 had the most effect to the wave functions. The parameters 𝑛𝑚𝑎𝑥, 𝑇, and 𝛼 had effect to the vibrational partition function 𝑍, vibrational mean energy 𝑈, vibrational specific heat 𝐶, vibrational free energy 𝐹, and vibrational entropy 𝑆. Conclusions: From the results of this study, it can be concluded that the energy, radial wave function, and thermodynamic properties for diatomic molecules have been obtained using the Nikiforov Uvarov Functional Analysis (NUFA) method.

scholarly journals The Schrödinger Equation with Deng-Fan-Eckart Potential (DFEP): Nikiforov-Uvarov-Functional Analysis (NUFA) Method

2021 ◽  
Vol 3 (5) ◽  
pp. 58-62
Author(s):  
E. B. Ettah
Keyword(s):  
Functional Analysis ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Energy Spectra ◽  
Analysis Method ◽  
Radial Part ◽  
Molecular Physics ◽  
Centrifugal Barrier ◽  
Eckart Potential ◽  
Good Agreement

In this study, the radial part of the Schrödinger equation with the Deng-Fan-Eckart potential (DFEP) is solved analytically by employing the improved Greene and Aldrich approximation to bypass the centrifugal barrier and using the Nikiforov-Uvarov-Functional Analysis method (NUFA). The energy expression and wave function are obtained respectively. The numerical energy spectra for some diatomic molecules have been studied and compared with the findings of earlier studies and it has been found to be in good agreement. The NUFA method used in this study is easy and very less cumbersome compared to other methods that currently exist and it is recommended that researchers in this area adopt this method. The findings of this study will find direct applications in molecular physics.

scholarly journals ANALYTICAL SOLUTION OF SCHRÖDINGER EQUATION FOR YUKAWA POTENTIAL WITH VARIABLE MASS IN TOROIDAL COORDINATE USING SUPERSYMMETRIC QUANTUM MECHANICS

2020 ◽  
Vol 17 (35) ◽  
pp. 100-108
Author(s):  
Suci FANIANDARI ◽  
A. SUPARMI ◽  
C. CARI
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Yukawa Potential ◽  
Radial Wave Function ◽  
Variable Mass ◽  
Energy Spectra ◽  
Radial Wave ◽  
Infinite Dimensional ◽  
Quantum Numbers

Schrodinger equation on a toroidal coordinate was proposed in theoretical physics to get the information and the behavior of the system of particle. It was solved just recently in case of a charged scalar particle interacting with a uniform magnetic field, a uniform electric field, and a neutral charge constrained to the surface. The methodology used in the referred work was to solve the Schrodinger equation using an approach outlined in the Whittaker-Watson treatise, which deals with an infinite-dimensional eigenvalue problem and specific particular values of the applied field for eigenfunction problem. In contrast, in the quantum mechanical problem, one had an infinite-dimensional generalized eigenvalue problem. This study aimed to obtain the non-relativistic energy eigenvalue and the radial wave function of the Schrodinger equation under the influence of Yukawa potential. The Supersymmetric Quantum Mechanics (SUSY QM) method was used as a basis to tackle the primary objective of this paper to study the problem of a particle with variable mass in toroidal coordinate. The proper super potential was used to deal with the hyperbolic form of effective potential, and the energy spectra were calculated for different quantum numbers, potential depth, and potential parameters. The radial wave function equation for ground and excited state were obtained. The results showed that the increasing value of the quantum numbers caused the energy spectra of the system to increase to the highest value when the quantum number was equal to the potential parameter, which means the most effective energy value was produced, then it was decreased afterward. While the energy value did not depend on the change of the potential parameter. This property could be used to produce this equation as an application of the previous results, the Schrödinger eigenfunction was used as the starting points to solve the other equation in the same geometrical setting and potential.

scholarly journals Exact Solution of Schrödinger Equation with Inverted Woods-Saxon and Manning-Rosen Potentials

2010 ◽  
Vol 3 (1) ◽  
pp. 25 ◽  
Author(s):  
A. N. Ikot ◽  
L. E. Akpabio ◽  
E. B. Umoren
Keyword(s):  
Exact Solution ◽  
Wave Function ◽  
Energy Spectrum ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Negative Energy ◽  
Dinger Equation ◽  
Radial Schrödinger Equation ◽  
Rosen Potential

We have analytically solved the radial Schrödinger equation with inverted Woods-Saxon and Manning-Rosen Potentials. With the ansatz for the wave function, we obtain the generalized wave function and the negative energy spectrum for the system.Keywords: Inverted Woods-Saxon Potentials; Manning-Rosen Potential; Schrödinger Equation.© 2011 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi:10.3329/jsr.v3i1.5310                J. Sci. Res. 3 (1), 25-33 (2011)

scholarly journals Approximate Solutions of Schrodinger Equation with Some Diatomic Molecular Interactions Using Nikiforov-Uvarov Method

2017 ◽  
Vol 2017 ◽  
pp. 1-24 ◽  
Author(s):  
Ituen B. Okon ◽  
Oyebola Popoola ◽  
Cecilia N. Isonguyo
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Yukawa Potential ◽  
Diatomic Molecules ◽  
Bound State ◽  
Spectroscopic Constant ◽  
Expectation Values ◽  
Quadratic Potential ◽  
Uvarov Method

We used a tool of conventional Nikiforov-Uvarov method to determine bound state solutions of Schrodinger equation with quantum interaction potential called Hulthen-Yukawa inversely quadratic potential (HYIQP). We obtained the energy eigenvalues and the total normalized wave function. We employed Hellmann-Feynman Theorem (HFT) to compute expectation values r-2, r-1, T, and p2 for four different diatomic molecules: hydrogen molecule (H2), lithium hydride molecule (LiH), hydrogen chloride molecule (HCl), and carbon (II) oxide molecule. The resulting energy equation reduces to three well-known potentials which are as follows: Hulthen potential, Yukawa potential, and inversely quadratic potential. The bound state energies for Hulthen and Yukawa potentials agree with the result reported in existing literature. We obtained the numerical bound state energies of the expectation values by implementing MATLAB algorithm using experimentally determined spectroscopic constant for the different diatomic molecules. We developed mathematica programming to obtain wave function and probability density plots for different orbital angular quantum number.

Solusi Persamaan Schrödinger Berbasis Panjang Minimal untuk Potensial Coulomb Termodifikasi

2018 ◽  
Vol 2 (2) ◽  
pp. 43-47
Author(s):  
A. Suparmi, C. Cari, Ina Nurhidayati
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Minimal Length ◽  
Energy Spectra ◽  
Atomic Particle ◽  
Approximate Analytical Solutions ◽  
Radial Schrödinger Equation

Abstrak – Persamaan Schrödinger adalah salah satu topik penelitian yang yang paling sering diteliti dalam mekanika kuantum. Pada jurnal ini persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Fungsi gelombang dan spektrum energi yang dihasilkan menunjukkan kharakteristik atau tingkah laku dari partikel sub atom. Dengan menggunakan metode pendekatan hipergeometri, diperoleh solusi analitis untuk bagian radial persamaan Schrödinger berbasis panjang minimal diaplikasikan untuk potensial Coulomb Termodifikasi. Hasil yang diperoleh menunjukkan terjadi peningkatan energi yang sebanding dengan meningkatnya parameter panjang minimal dan parameter potensial Coulomb Termodifikasi. Kata kunci: persamaan Schrödinger, panjang minimal, fungsi gelombang, energi, potensial Coulomb Termodifikasi Abstract – The Schrödinger equation is the most popular topic research at quantum mechanics. The  Schrödinger equation based on the concept of minimal length formalism has been obtained for modified Coulomb potential. The wave function and energy spectra were used to describe the characteristic of sub-atomic particle. By using hypergeometry method, we obtained the approximate analytical solutions of the radial Schrödinger equation based on the concept of minimal length formalism for the modified Coulomb potential. The wave function and energy spectra was solved. The result showed that the value of energy increased by the increasing both of minimal length parameter and the potential parameter. Key words: Schrödinger equation, minimal length formalism (MLF), wave function, energy spectra, Modified Coulomb potential

COLLECTIVE SPIN BY LINEARIZATION OF THE SCHRÖDINGER EQUATION FOR NUCLEAR COLLECTIVE MOTION

1988 ◽  
Vol 03 (09) ◽  
pp. 859-866 ◽  
Author(s):  
MARTIN GREINER ◽  
WERNER SCHEID ◽  
RICHARD HERRMANN
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Degrees Of Freedom ◽  
Collective Motion ◽  
First Order ◽  
Energy And Momentum

The free Schrödinger equation for multipole degrees of freedom is linearized so that energy and momentum operators appear only in first order. As an example, we demonstrate the linearization procedure for quadrupole degrees of freedom. The wave function solving this equation carries a spin. We derive the operator of the collective spin and its eigenvalues depending on multipolarity.

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