Solution of Radial Schrödinger Equation with Yukawa Potential Using Bethe Ansatz Method

We apply the asymptotic iteration method to solve the radial Schrödinger equation for the Yukawa type potentials. The solution of the radial Schrödinger equation by using different approaches requires tedious and cumbersome calculations; however, we present that it is possible to obtain the bound state energy eigenvalues for any n and ℓ values easily within the framework of this method. We also show the perturbed application of this method for the same potential. Our results are in excellent agreement with the findings of the SUSY perturbation, 1/N expansion and numerical methods.

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

Revista Mexicana de Física ◽

10.31349/revmexfis.67.482 ◽

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.

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Solusi Persamaan Schrödinger Berbasis Panjang Minimal untuk Potensial Coulomb Termodifikasi

Risalah Fisika ◽

10.35895/rf.v2i2.117 ◽

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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