An analytical solution of the time-independent Schrödinger equation for the Woods-Saxon potential for arbitrary angular momentum l states

2015 ◽  
Author(s):  
P. Rajesh Kumar ◽  
B. R. Wong
Keyword(s):  
Angular Momentum ◽  
Analytical Solution ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Saxon Potential

Bound state solution of the Schrodinger equation for the Woods–Saxon potential plus coulomb interaction by Nikiforov–Uvarov and supersymmetric quantum mechanics methods

2021 ◽  
pp. 2150023
Author(s):  
Enayatolah Yazdankish
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Coulomb Interaction ◽  
Schrodinger Equation ◽  
Energy Eigenvalue ◽  
Bound State ◽  
Repulsive Interaction ◽  
Saxon Potential ◽  
Special Cases ◽  
Supersymmetry Quantum Mechanics

The generalized Woods–Saxon potential plus repulsive Coulomb interaction is considered in this work. The supersymmetry quantum mechanics method is used to get the energy spectrum of Schrodinger equation and also the Nikiforov–Uvarov approach is employed to solve analytically the Schrodinger equation in the framework of quantum mechanics. The potentials with centrifugal term include both exponential and radial terms, hence, the Pekeris approximation is considered to approximate the radial terms. By using the step-by-step Nikiforov–Uvarov method, the energy eigenvalue and wave function are obtained analytically. After that, the spectrum of energy is obtained by the supersymmetry quantum mechanics method. The energy eigenvalues obtained from each method are the same. Then in special cases, the results are compared with former result and a full agreement is observed. In the [Formula: see text]-state, the standard Woods–Saxon potential has no bound state, but with Coulomb repulsive interaction, it may have bound state for zero angular momentum.

Solving of the Schrodinger equation analytically with an approximated scheme of the Woods–Saxon potential by the systematical method of Nikiforov–Uvarov

2020 ◽  
Vol 29 (06) ◽  
pp. 2050032
Author(s):  
Enayatolah Yazdankish
Keyword(s):  
Schrödinger Equation ◽  
Exponential Type ◽  
Schrodinger Equation ◽  
Analytic Solutions ◽  
Centrifugal Term ◽  
Saxon Potential ◽  
Energy Eigenvalues ◽  
Nu Method

The analytic solutions of the Schrodinger equation for the Woods–Saxon (WS) potential and also for the generalized WS potential are obtained for the [Formula: see text]-wave nonrelativistic spectrum, with an approximated form of the WS potential and centrifugal term. Due to this fact that the potential is an exponential type and the centrifugal is a radial term, we have to use an approximated scheme. First, the Nikiforov–Uvarov (NU) method is introduced in brief, which is a systematical method, and then Schrodinger equation is solved analytically. Energy eigenvalues and the corresponding eigenvector are derived analytically by using the NU method. After that, the generalized WS potential is discussed at the end.

Three and Four Centre Oscillators and Their Application in Nuclear Physics

1974 ◽  
Vol 29 (7) ◽  
pp. 1003-1010 ◽  
Author(s):  
Peter Bergmann ◽  
Hans-Joachim Scheefer
Keyword(s):  
Analytical Solution ◽  
Schrödinger Equation ◽  
Nuclear Physics ◽  
Schrodinger Equation ◽  
Numerical Procedure ◽  
Orthogonal Basis ◽  
Two Dimensional ◽  
Schmidt's Method ◽  
Symmetry Properties

The extension of the nuclear two-centre-oscillator to three and four centres is investigated. Some special symmetry-properties are required. In two cases an analytical solution of the Schrödinger equation is possible. A numerical procedure is developed which enables the diagonalization of the Hamiltonian in a non-orthogonal basis without applying Schmidt's method of orthonormalization. This is important for calculations of arbitrary two-dimensional arrangements of the centres.

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