scholarly journals The Analytical Solutions of the Schrodinger Equation for a Single Electron in the Nikiforov-Uvarov Framework

Jurnal Fisika ◽  
2020 ◽  
Vol 10 (2) ◽  
pp. 1-10
Author(s):  
Yacobus Yulianto ◽  
Zaki Su'ud
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Analytical Solutions ◽  
Schrodinger Equation ◽  
Quantum Physics ◽  
Energy Eigenvalue ◽  
Single Electron ◽  
Alternative Procedure ◽  
Alternative Method ◽  
Uvarov Method

In this study, it is intended to show an alternative method to derive the wave function of a single electron as solutions of the Schrodinger equation. The Nikiforov-Uvarov method was chosen to be utilized since this method can solve the Schrodinger equation with several well-known potentials in the non-relativistic mechanics of quantum. The obtained results of this study have succeed to explain the wave function and the energy eigenvalue for a single electron as lectured in quantum physics textbooks. These results prove that the Nikiforov-Uvarov method provides an alternative procedure to solve the Schrodinger equation.

scholarly journals Bound State Solutions of the Hua Potential within the Framework of Two Approximations Scheme

2021 ◽  
Vol 3 (3) ◽  
pp. 38-41
Author(s):  
E. B. Ettah ◽  
P. O. Ushie ◽  
C. M. Ekpo
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Energy Equation ◽  
Bound State ◽  
S Wave ◽  
Angular Momenta ◽  
Special Cases ◽  
Uvarov Method

In this paper, we solve analytically the Schrodinger equation for s-wave and arbitrary angular momenta with the Hua potential is investigated respectively. The wave function as well as energy equation are obtained in an exact analytical manner via the Nikiforov Uvarov method using two approximations scheme. Some special cases of this potentials are also studied.

scholarly journals ANALYTICAL SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH THE MANNING–ROSEN POTENTIAL PLUS A RING-SHAPED-LIKE POTENTIAL

2013 ◽  
Vol 22 (10) ◽  
pp. 1350072 ◽  
Author(s):  
H. I. AHMADOV ◽  
C. AYDIN ◽  
N. SH. HUSEYNOVA ◽  
O. UZUN
Keyword(s):  
Analytical Solution ◽  
Schrödinger Equation ◽  
Orthogonal Polynomials ◽  
Analytical Solutions ◽  
Schrodinger Equation ◽  
Approximation Scheme ◽  
Energy Levels ◽  
Rosen Potential ◽  
Uvarov Method

The analytical solution of the Schrödinger equation for the Manning–Rosen potential plus a ring-shaped-like potential is obtained by applying the Nikiforov–Uvarov method by using the improved approximation scheme to the centrifugal potential for arbitrary l states. The energy levels are worked out and the corresponding normalized eigenfunctions are obtained in terms of orthogonal polynomials for arbitrary l states.

Calculation of Masses of Di-Mesons Consisting of a Pair of Heavy Mesons

2020 ◽  
Vol 35 (14) ◽  
pp. 2050109
Author(s):  
P. Sadeghi Alavijeh ◽  
N. Tazimi ◽  
M. Monemzadeh
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Root Mean Square ◽  
Schrodinger Equation ◽  
Binding Energies ◽  
Mean Square ◽  
Heavy Mesons ◽  
Coulomb Type ◽  
Uvarov Method ◽  
Type Potential

In this paper, we study four-quark states as di-hadronic molecular states. For this purpose, we apply the Nikiforov–Uvarov method to solve the Schrödinger equation in the presence of the Woods–Saxon plus Coulomb-type potential and we obtain the binding energies and masses of heavy di-mesons. We calculate the root mean square (r.m.s) radius and the wave function for some observed tetraquarks.

scholarly journals SOLVING THE SCHRÖDINGER EQUATION FOR BOUND STATES WITH MATHEMATICA 3.0

1999 ◽  
Vol 10 (04) ◽  
pp. 607-619 ◽  
Author(s):  
WOLFGANG LUCHA ◽  
FRANZ F. SCHÖBERL
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Interaction Potential ◽  
Schrodinger Equation ◽  
Bound States ◽  
Energy Eigenvalue ◽  
Wave Functions ◽  
Spherically Symmetric ◽  
Method Of Solution ◽  
Numerical Integration Procedure

Using Mathematica 3.0, the Schrödinger equation for bound states is solved. The method of solution is based on a numerical integration procedure together with convexity arguments and the nodal theorem for wave functions. The interaction potential has to be spherically symmetric. The solving procedure is simply defined as some Mathematica function. The output is the energy eigenvalue and the reduced wave function, which is provided as an interpolated function (and can thus be used for the calculation of, e.g., moments by using any Mathematica built-in function) as well as plotted automatically. The corresponding program schroedinger.nb can be obtained from [email protected].

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

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