scholarly journals WKB Energy Expression for the Radial Schrödinger Equation with a Generalized Pseudoharmonic Potential

2020 ◽  
pp. 13-20 ◽  
Author(s):  
E. Omugbe ◽  
O. E. Osafile ◽  
I. B. Okon
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Turning Points ◽  
Wkb Method ◽  
Energy Expression ◽  
Pseudoharmonic Potential ◽  
Special Cases ◽  
Radial Schrödinger Equation ◽  
Exact Energy

In this paper, we applied the semi-classical quantization approximation method to solve the radial Schrödinger equation with a generalized Pseudoharmonic potential. The four turning points problem within the framework of the Wentzel-Kramers-Brillouin (WKB) method was transformed into two turning points and subsequently, the energy spectrum was obtained. Some special cases of the generalized Pseudoharmonic potential are presented. The WKB approximation approach reproduces the exact energy expression obtained with several analytical methods in the literature.  The values of the energy levels for some selected diatomic molecules (N2, CO, NO, CH) obtained numerically are in excellent agreement with those from previous works in the literature.

scholarly journals Exact Analytical Solution of theN-Dimensional Radial Schrödinger Equation with Pseudoharmonic Potential via Laplace Transform Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Tapas Das ◽  
Altuğ Arda
Keyword(s):  
Schrödinger Equation ◽  
Laplace Transform ◽  
Schrodinger Equation ◽  
Exact Analytical Solution ◽  
Bound State ◽  
Pseudoharmonic Potential ◽  
Special Cases ◽  
Radial Schrödinger Equation ◽  
The Laplace Transform ◽  
Generalized Morse Potential

The second-orderN-dimensional Schrödinger equation with pseudoharmonic potential is reduced to a first-order differential equation by using the Laplace transform approach and exact bound state solutions are obtained using convolution theorem. Some special cases are verified and variations of energy eigenvaluesEnas a function of dimensionNare furnished. To give an extra depth of this paper, the present approach is also briefly investigated for generalized Morse potential as an example.

A new determination of the parameters of the optimized Heine–Abarenkov potential for 27 elements

1976 ◽  
Vol 54 (23) ◽  
pp. 2348-2354 ◽  
Author(s):  
E. R. Cowley
Keyword(s):  
Schrödinger Equation ◽  
Numerical Integration ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Inhomogeneity Correction ◽  
Radial Schrödinger Equation

We have calculated the energy levels of the truncated Coulomb potential using numerical integration of the radial Schrödinger equation, rather than interpolation in tables. The results are used to give the parameters of the optimized Heine–Abarenkov potential for 27 elements. Various methods of weighting other contributions to the potential in the solid are used, and the inhomogeneity correction introduced by Ballentine and Gupta is discussed.

scholarly journals Fourth derivative singularly P-stable method for the numerical solution of the Schrödinger equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ali Shokri ◽  
Higinio Ramos ◽  
Mohammad Mehdizadeh Khalsaraei ◽  
Fikret A. Aliev ◽  
Martin Bohner
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Stable Method ◽  
Implicit Methods ◽  
The Family ◽  
Radial Schrödinger Equation ◽  
Obrechkoff Methods ◽  
Fourth Derivative ◽  
Error Terms

AbstractIn this paper, we construct a method with eight steps that belongs to the family of Obrechkoff methods. Due to the explicit nature of the new method, not only does it not require another method as predictor, but it can also be considered as a suitable predictive technique to be used with implicit methods. Periodicity and error terms are studied when applied to solve the radial Schrödinger equation, considering different energy levels. We show its advantages in terms of accuracy, consistency, and convergence in comparison with other methods of the same order appearing in the literature.

ANALYTICAL APPROXIMATIONS TO THE l-WAVE SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH A HYPERBOLIC POTENTIAL

2008 ◽  
Vol 22 (07) ◽  
pp. 483-489 ◽  
Author(s):  
SHISHAN DONG ◽  
S. G. MIRANDA ◽  
F. M. ENRIQUEZ ◽  
SHI-HAI DONG
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Bound State ◽  
Short Range Potential ◽  
Quantum Numbers ◽  
Analytical Approximations ◽  
Special Cases ◽  
Hyperbolic Potential ◽  
Arbitrary Quantum

The bound-state solutions of the Schrödinger equation for a hyperbolic potential with the centrifugal term are presented approximately. It is shown that the solutions can be expressed by the hypergeometric function 2F1(a, b; c; z). To show the accuracy of our results, we calculate the energy levels numerically for arbitrary quantum numbers n and l. It is found that the results are in good agreement with those obtained by other methods for short-range potential. Two special cases for l = 0 and σ = 1 are also studied briefly.

scholarly journals Arbitrary l-solutions of the Schrödinger equation interacting with Hulthén – Hellmann potential model

2020 ◽  
Vol 66 (6 Nov-Dec) ◽  
pp. 730 ◽  
Author(s):  
E. S. William ◽  
E. P. Inyang ◽  
E. A. Thompson
Keyword(s):  
Schrödinger Equation ◽  
Quantum State ◽  
Schrodinger Equation ◽  
Potential Model ◽  
Bound State ◽  
Energy Eigenvalues ◽  
Special Cases ◽  
Radial Schrödinger Equation ◽  
Hellmann Potential ◽  
Good Agreement

In this study, we obtained bound state solutions of the radial Schrödinger equation by the superposition of Hulthén plus Hellmann potential within the framework of Nikiforov-Uvarov (NU) method for an arbitrary  - states. The corresponding normalized wave functions expressed in terms of Jacobi polynomial for a particle exposed to this potential field was also obtained. The numerical energy eigenvalues for different quantum state have been computed. Six special cases are also considered and their energy eigenvalues are obtained. Our results are found to be in good agreement with the results in literature. The behavior of energy in the ground and excited state for different quantum state are studied graphically.

scholarly journals Exact Solution of the Schrödinger Equation for Composition of Coulomb and Oscillator Potentials

2021 ◽  
Vol 24 (2) ◽  
pp. 203-206
Author(s):  
V. V. Kudryashov ◽  
A. V. Baran
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Hypergeometric Functions ◽  
Continuous Solution ◽  
Energy Levels ◽  
Discrete Energy ◽  
Radial Wave ◽  
Confluent Hypergeometric Functions ◽  
Radial Schrödinger Equation ◽  
Boundary Distance

The spherically symmetric potential is considered whose dependence on the distance r is described by the smooth composition of Coulomb at r < r0 and oscillator at r > r0 potentials. The boundary distance r0 is determined by the parameters of these potentials. The exact continuous solution of the radial Schrödinger equation is expressed in terms of the confluent hypergeometric functions. The discrete energy levels are obtained. The graphic illustrations for the energy spectrum and the radial wave functions are presented.

scholarly journals Analytical solutions of the Schrödinger equation for the Hulthén potential within SUSY quantum mechanics

2015 ◽  
Vol 30 (32) ◽  
pp. 1550193 ◽  
Author(s):  
H. I. Ahmadov ◽  
Sh. I. Jafarzade ◽  
M. V. Qocayeva
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Hulthén Potential ◽  
Shape Invariance ◽  
Hulthen Potential ◽  
Radial Schrödinger Equation ◽  
Uvarov Method ◽  
Ordinary Quantum

The analytical solution of the modified radial Schrödinger equation for the Hulthén potential is obtained within ordinary quantum mechanics by applying the Nikiforov–Uvarov method and supersymmetric quantum mechanics by applying the shape invariance concept that was introduced by Gendenshtein 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.

scholarly journals Approximate solutions of the Schrödinger equation with Hulthén-Hellmann Potentials for a Quarkonium system

2021 ◽  
Vol 67 (3 May-Jun) ◽  
pp. 482
Author(s):  
I. O. Akpan ◽  
E. P. Inyang ◽  
E. P Inyang ◽  
E. S. William
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Yukawa Potential ◽  
Laguerre Polynomials ◽  
Approximate Solutions ◽  
Heavy Mesons ◽  
Special Cases ◽  
Radial Schrödinger Equation ◽  
Hellmann Potential ◽  
Uvarov Method

Hulthén plus Hellmann potentials are adopted as the quark-antiquark interaction potential for studying the mass spectra of heavy mesons. We solved the radial Schrödinger equation analytically using the Nikiforov-Uvarov method. The energy eigenvalues and corresponding wave function in terms of Laguerre polynomials were obtained. The present results are applied for calculating the mass of heavy mesons such as charmonium and bottomonium. Four special cases were considered when some of the potential parameters were set to zero, resulting into Hellmann potential, Yukawa potential, Coulomb potential, and Hulthén potential, respectively. The present potential provides satisfying results in comparison with experimental data and the work of other researchers.

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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