New WKB Approximate Solution of the Radial Schrödinger Equation Finite at the Turning Points

AbstractIn this paper we consider a methodology of optimization of the efficiency of a numerical method for the approximate solution of the radial Schrödinger equation and related problems. More specifically, we show how the methodology of vanishing of the phase-lag and its derivatives optimizes the behaviour of a numerical method.

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

Asian Journal of Physical and Chemical Sciences ◽

10.9734/ajopacs/2020/v8i230112 ◽

2020 ◽

pp. 13-20 ◽

Cited By ~ 2

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.

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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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