scholarly journals Determine the Eigen Function of Schrodinger Equation with Non-Central Potential by Using NU Method

2011 ◽  
Vol 02 (08) ◽  
pp. 999-1004 ◽  
Author(s):  
Hamdollah Salehi
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Central Potential ◽  
Nu Method ◽  
Eigen Function

scholarly journals The spinless relativistic kink-like problem

2015 ◽  
Vol 30 (12) ◽  
pp. 1550062 ◽  
Author(s):  
Wolfgang Lucha ◽  
Franz F. Schöberl
Keyword(s):  
Quantum Theory ◽  
Eigenvalue Problem ◽  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Schrodinger Equation ◽  
Bound State ◽  
State Equation ◽  
Hyperbolic Tangent ◽  
Central Potential ◽  
All Solutions

We constrain the possible bound-state solutions of the spinless Salpeter equation (the most obvious semirelativistic generalization of the nonrelativistic Schrödinger equation) with an interaction between the bound-state constituents given by the kink-like potential (a central potential of hyperbolic-tangent form) by formulating a bunch of very elementary boundary conditions to be satisfied by all solutions of the eigenvalue problem posed by a bound-state equation of this type, only to learn that all results produced by a procedure very much liked by some quantum-theory practitioners prove to be in severe conflict with our expectations.

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.

scholarly journals Solusi Persamaan Schrödinger untuk Potensial Hulthen + Non-Sentral Poschl-Teller dengan Menggunakan Metode Nikiforov-Uvarov

2016 ◽  
Vol 3 (02) ◽  
pp. 169
Author(s):  
Nani Sunarmi ◽  
Suparmi S ◽  
Cari C
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Jacobi Polynomials ◽  
Energy Levels ◽  
Hulthén Potential ◽  
Central Potential ◽  
Hulthen Potential ◽  
Hypergeometric Type ◽  
Angular Equation ◽  
Uvarov Method

<span>The Schrödinger equation for Hulthen potential plus Poschl-Teller Non-Central potential is <span>solved analytically using Nikiforov-Uvarov method. The radial equation and angular equation <span>are obtained through the variable separation. The solving of Schrödinger equation with <span>Nikivorov-Uvarov method (NU) has been done by reducing the two order differensial equation <span>to be the two order differential equation Hypergeometric type through substitution of <span>appropriate variables. The energy levels obtained is a closed function while the wave functions <span>(radial and angular part) are expressed in the form of Jacobi polynomials. The Poschl-Teller <span>Non-Central potential causes the orbital quantum number increased and the energy of the <span>Hulthen potential is increasing positively.</span></span></span></span></span></span></span></span><br /></span>

On the corrector formulas for the numerical solution of the Schrödinger equation for central fields

1966 ◽  
Vol 62 (1) ◽  
pp. 79-82 ◽  
Author(s):  
L. Lovitch ◽  
S. Rosati
Keyword(s):  
Differential Equation ◽  
Schrödinger Equation ◽  
Numerical Solution ◽  
Nuclear Physics ◽  
Schrodinger Equation ◽  
Numerical Evaluation ◽  
Good Precision ◽  
Initial Value ◽  
Central Potential ◽  
Standard Integration

The evaluation of the eigenvalues and corresponding solutions of a Schrödinger equation is an ever-present problem in atomic and nuclear physics. For the numerical evaluation of the Schrödinger equation for a particle in a central potential, a useful corrector formula was derived by Douglas and Ridley ((5)) some years ago. Given a first estimate of the eigenvalue, this formula enables one to obtain a better estimate using any standard integration procedure for the differential equation. In a particular example, it was found ((5)) that it was necessary to start with an initial value which was accurate to about 10% in order that the procedure should converge to the desired eigenvalue, and that few iterations were required to obtain the eigenvalue with good precision.

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