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AIP conference proceedings

Solution of Schrodinger equation with q-deformed momentum in Coulomb potential using hypergeometric method

Dyah Ayu Dianawati, Suparmi Suparmi, C. Cari

Published Jan 1, 2018• 3 citations
Publisher

Abstract

The Hypergeometric method was used to describe radial equations by probeneus approaximation at a singular regular point. Schrodinger equations radial part was reduced into differential equations with variable substitution. By using q-deformed momentum parameter and Coulomb potential as well as variable substitution, the second order of Schrodinger equation with centrifugal approach for q-deformed momentum in Coulomb potential can be solved with Hypergeometric method. The analytical result of energy spectrum and wave function with quantum number and q-deformed variations, while the numerical result for energy spectrum can be calculated by using Matlab 2013 software.

DOI
10.1063/1.5054475

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The Hypergeometric method was used to describe radial equations by probeneus approaximation at a singular regular point. Schrodinger equations radial part was reduced into differential equations with variable substitution. By using q-deformed momentum parameter and Coulomb potential as well as variable substitution, the second order of Schrodinger equation with centrifugal approach for q-deformed momentum in Coulomb potential can be solved with Hypergeometric method. The analytical result of energy spectrum and wave function with quantum number and q-deformed variations, while the numerical result for energy spectrum can be calculated by using Matlab 2013 software.
The Hypergeometric method was used to obtain the solution of Schrodinger equation for radial quantum deformation on Coulomb potential. The Schrodinger equation was reduced into the general form of Hypergeometric function with variable and parameter substitutions. As a result, the energy was calculated from the energy equation and wave function was visualized by Matlab R2013a software. The decrease of energy values causes the increase of quantum number and quantum deformation parameters, while the wave functions have the depth of deep amplitude by the increase of quantum number and quantum number parameters.
Abstract Hypergeometric method was used to obtain the solution of Klein-Gordon equation with q-deformed quantum mechanics for Coulomb potential. By introduction the new variable and parameters in the Klein-Gordon equation, then Klein-Gordon equation reduced to the second order differential equation of Hypergeometric function. From the solution of the Hypergeometric differential equation, the energy and wave function equations were obtained analytically. The energy was numerically calculated by Matlab R2013a software and the first three wave function was obtained. The result shows that the decrease of quantum deformation caused the increase of the energy eigen value, and the increase of quantum number caused the increase of the energy eigen value too.
The Schrodinger equation with quantum deformation for three-dimensional Harmonic Oscillator plus Inverse Quadratic potential was obtained the solution by Hypergeometric method with substituting variable and parameter to reduce Schrodinger equation into second order Hypergeometric differential equation.The non-relativistic energy was obtained from condition a=-n and wave function was expressed by Hypergeometric function.The results were calculated and visualized by Matlab R2013a software.The energy spectrum and wave function depend on the quantum deformation and quantum number parameters.
Hypergeometric method can be used to solve D-dimensional Klein-Gordon equation with q-deformed of radial momentum for Kratzer potential. By substituting q-deformed of radial momentum variable, the D-dimensional and the potential parameters to obtain the second order of D-dimensional Klein-Gordon equation which is used to determine the energy and wave function equations. The analytical result of energy can be founded with D-dimension and q-deformed of radial momentum variations. As a result, the rise of D-dimension values cause the rise of energy values, while the rice of q deformation values causes the decline of energy values.
The Q-deformed D-dimensional Klein Gordon equation with Kratzer potential is solved by using Hypergeometric method in the case of exact spin symmetry. The linear radial momentum of D-dimensional Klein Gordon equation is disturbed by the presence of the quadratic radial posisiton. The Klein-Gordon D-dimensional equation is reduced to one-dimensional Schrodinger like equation with variable substitution. The solution of the D-dimensional Klein-Gordon equation is determined in the form of a general equation of the Hypergeometry function using the Kratzer potential variable and the quantum deformation variable. From this equation, relativistic energy and wave function are determined. In addition, the relativistic energy equation can be used to calculate numerical energy levels for diatomic particles (CO, NO, O2) using Matlab R2013a software. The results obtained show that the q-deformed quantum parameters, quantum numbers and dimensions affect the value of relativistic energy for zero-pin particles. The value of energy increases with increasing value of quantum number n, q-deformed parameters, and d-dimensional parameters. Of the three parameters, q-deformed parameter is the most dominant to give change in energy value; the increasing q-deformed parameter causes the energy value increases significantly compared to the d-dimensional parameter and quantum numbers n.
Spatially quadratic deformation radial momentum of D-dimensional Klein-Gordon equation with three-dimensional Harmonic Oscillator and Inverse Quadratic potential was investigated using Hypergeometric Method. By using appropriate variable transformation, D-Dimensional Klein-Gordon equation for q deformed momentum was reduced into one order dimensional Schrodinger like equation with Pöschl-Teller like potential. The relativistic energy and wave function equations were obtained from the solution of Schrodinger like equation. Then, the relativistic energy and wave function were calculated and visualized using Matlab R2013 software, respectively. The q deformed parameter had the effect to the relativistic energy and wave function. The increase of q deformed parameter causes the increase of energy spectra and the decrease of amplitude.