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Approximate eigensolutions of the attractive potential via parametric Nikiforov-Uvarov method
C A Onate1, O Adebimpe1, A F Lukman1
1Department of Physical Sciences, Landmark University, Omu-Aran, PMB 1001, Omu Aran, Kwara, Nigeria.
Heliyon
|February 15, 2019
Summary
We solved the Schrӧdinger equation for an attractive potential using the parametric Nikiforov-Uvarov method. Energy levels and wave functions were found, showing sensitivity to potential parameters.
Area of Science:
- Quantum mechanics
- Mathematical physics
Background:
- The non-relativistic Schrӧdinger equation is fundamental in quantum mechanics.
- Analytical solutions for potentials with centrifugal terms are often challenging.
Purpose of the Study:
- To find approximate analytical solutions for the Schrӧdinger equation with an attractive potential and centrifugal term.
- To investigate the influence of potential parameters on energy levels.
Main Methods:
- Parametric Nikiforov-Uvarov method.
- Greene-Aldrich approximation scheme.
Main Results:
- Obtained energy equation and un-normalized radial wave functions in a compact form.
- Investigated special cases and the impact of potential strengths and range on energy.
- Energy levels demonstrated high sensitivity to potential parameters.
Conclusions:
- The parametric Nikiforov-Uvarov method provides an effective approach for solving the Schrӧdinger equation.
- Understanding the behavior of energy levels is crucial for potential model applications.
Keywords:
Quantum mechanics
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