scholarly journals Bound state solutions of the Manning–Rosen potential

2013 ◽  
Vol 91 (1) ◽  
pp. 98-104 ◽  
Author(s):  
B.J. Falaye ◽  
K.J. Oyewumi ◽  
T.T. Ibrahim ◽  
M.A. Punyasena ◽  
C.A. Onate
Keyword(s):  
Bound State ◽  
Approximation Schemes ◽  
Asymptotic Iteration Method ◽  
S Wave ◽  
Quantum Numbers ◽  
Analytical Approximations ◽  
Potential Case ◽  
Rosen Potential ◽  
Arbitrary Quantum ◽  
Good Agreement

Using the asymptotic iteration method (AIM), we have obtained analytical approximations to the ℓ-wave solutions of the Schrödinger equation with the Manning–Rosen potential. The energy eigenvalues equation and the corresponding wavefunctions have been obtained explicitly. Three different Pekeris-type approximation schemes have been used to deal with the centrifugal term. To show the accuracy of our results, we have calculated the eigenvalues numerically for arbitrary quantum numbers n and ℓ for some diatomic molecules (HCl, CH, LiH, and CO). It is found that the results are in good agreement with other results found in the literature. A straightforward extension to the s-wave case and Hulthén potential case are also presented.

Energy spectrum for trigonometric Pöschl–Teller potential

2012 ◽  
Vol 90 (12) ◽  
pp. 1259-1265 ◽  
Author(s):  
Babatunde James Falaye
Keyword(s):  
Bound State ◽  
Asymptotic Iteration Method ◽  
Generalized Hypergeometric Functions ◽  
Short Range Potential ◽  
Energy Eigenvalues ◽  
Molecular Potential ◽  
Quantum Numbers ◽  
Special Case ◽  
Arbitrary Quantum ◽  
Good Agreement

We present analytical solutions of the Schrödinger equation for the trigonometric Pöschl–Teller molecular potential by using a proper approximation to the centrifugal term within the framework of the asymptotic iteration method. We obtain analytic forms for the energy eigenvalues and the bound state eigenfunction solutions are obtained in terms of the generalized hypergeometric functions. Energy eigenvalues for a few diatomic molecules are calculated for arbitrary quantum numbers n and ℓ with various values of parameter α. We also studied special case ℓ = 0 and found that the results are in good agreement with findings of other methods for short-range potential.

scholarly journals Approximate l-States of the Manning-Rosen Potential by Using Nikiforov-Uvarov Method

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Sameer M. Ikhdair
Keyword(s):  
Jacobi Polynomials ◽  
Bound State ◽  
Potential Range ◽  
Quantum Numbers ◽  
Special Cases ◽  
Screening Parameter ◽  
Potential Case ◽  
Rosen Potential ◽  
Uvarov Method ◽  
Good Agreement

The approximately analytical bound state solutions of the l-wave Schrödinger equation for the Manning-Rosen (MR) potential are carried out by a proper approximation to the centrifugal term. The energy spectrum formula and normalized wave functions expressed in terms of the Jacobi polynomials are both obtained for the application of the Nikiforov-Uvarov (NU) method to the Manning-Rosen potential. To show the accuracy of our results, we calculate the eigenvalues numerically for arbitrary principal and orbital quantum numbers n and l with two different values of the potential screening parameter α. It is found that our results are in good agreement with the those obtained by other methods for short potential range, lowest values of orbital quantum number l, and α. Two special cases of much interest are investigated like the s-wave case and Hulthén potential case.

ANALYTICAL APPROXIMATIONS TO THE SCHRÖDINGER EQUATION FOR A SECOND PÖSCHL–TELLER-LIKE POTENTIAL WITH CENTRIFUGAL TERM

2008 ◽  
Vol 23 (10) ◽  
pp. 1537-1544 ◽  
Author(s):  
SHI-HAI DONG ◽  
WEN-CHAO QIANG ◽  
J. GARCÍA-RAVELO
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound State ◽  
Centrifugal Term ◽  
Short Range Potential ◽  
Quantum Numbers ◽  
Analytical Approximations ◽  
Special Cases ◽  
Arbitrary Quantum ◽  
Good Agreement

The bound state solutions of the Schrödinger equation for a second Pöschl–Teller-like potential with the centrifugal term are obtained approximately. It is found that the solutions can be expressed in terms of the hypergeometric functions 2F1(a, b; c; z). To show the accuracy of our results, we calculate the eigenvalues numerically for arbitrary quantum numbers n and l. It is found that the results are in good agreement with those obtained by other method for short-range potential. Two special cases for l = 0 and V1 = V2 are also studied briefly.

ANALYTICAL APPROXIMATIONS TO THE l-WAVE SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH A HYPERBOLIC POTENTIAL

2008 ◽  
Vol 22 (07) ◽  
pp. 483-489 ◽  
Author(s):  
SHISHAN DONG ◽  
S. G. MIRANDA ◽  
F. M. ENRIQUEZ ◽  
SHI-HAI DONG
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Bound State ◽  
Short Range Potential ◽  
Quantum Numbers ◽  
Analytical Approximations ◽  
Special Cases ◽  
Hyperbolic Potential ◽  
Arbitrary Quantum

The bound-state solutions of the Schrödinger equation for a hyperbolic potential with the centrifugal term are presented approximately. It is shown that the solutions can be expressed by the hypergeometric function 2F1(a, b; c; z). To show the accuracy of our results, we calculate the energy levels numerically for arbitrary quantum numbers n and l. It is found that the results are in good agreement with those obtained by other methods for short-range potential. Two special cases for l = 0 and σ = 1 are also studied briefly.

Nonrelativistic and relativistic bound state solutions of the molecular Tietz potential via the improved asymptotic iteration method

2014 ◽  
Vol 92 (3) ◽  
pp. 215-220 ◽  
Author(s):  
W.A. Yahya ◽  
K. Issa ◽  
B.J. Falaye ◽  
K.J. Oyewumi
Keyword(s):  
Iteration Method ◽  
Vibrational Energy ◽  
Bound State ◽  
Asymptotic Iteration Method ◽  
Quantum Numbers ◽  
Approximate Analytical Solutions ◽  
Relative Closeness ◽  
Klein Gordon ◽  
Tietz Potential ◽  
Schrödinger System

We have obtained the approximate analytical solutions of the relativistic and nonrelativistic molecular Tietz potential using the improved asymptotic iteration method. By approximating the centrifugal term through the Greene–Aldrich approximation scheme, we have obtained the energy eigenvalues and wave functions for all orbital quantum numbers [Formula: see text]. Where necessary, we made comparison with the result obtained previously in the literature. The relative closeness of the two results reveal the accuracy of the method presented in this study. We proceed further to obtain the rotational-vibrational energy spectrum for some diatomic molecules. These molecules are CO, HCl, H2, and LiH. We have also obtained the relativistic bound state solution of the Klein−Gordon equation with this potential. In the nonrelativistic limits, our result converges to that of the Schrödinger system.

scholarly journals Tau decay into $$\nu _\tau $$ and $$a_1(1260)$$, $$b_1(1235)$$, and two $$K_1(1270)$$

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
L. R. Dai ◽  
L. Roca ◽  
E. Oset
Keyword(s):  
Axial Vector ◽  
S Wave ◽  
Decay Channels ◽  
Quantum Numbers ◽  
Present Information ◽  
Unitary Approach ◽  
One Step ◽  
Chiral Unitary Approach ◽  
Cabibbo Suppressed ◽  
Good Agreement

Abstract We study the $$\tau \rightarrow \nu _\tau A$$τ→ντA decay, with A an axial-vector meson. We produce the $$a_1(1260)$$a1(1260) and $$b_1(1235)$$b1(1235) resonances in the Cabibbo favored mode and two $$K_1(1270)$$K1(1270) states in the Cabibbo suppressed mode. We take advantage of previous chiral unitary approach results where these resonances appear dynamically from the vector and pseudoscalar meson interaction in s-wave. Actually two different poles were obtained associated to the $$K_1(1270)$$K1(1270) quantum numbers. We find that the unmeasured rates for $$b_1(1235)$$b1(1235) production are similar to those of the $$a_1(1260)$$a1(1260) and for the two $$K_1$$K1 states we suggest to separate the present information on the $$\bar{K} \pi \pi $$K¯ππ invariant masses into $$\bar{K}^* \pi $$K¯∗π and $$\rho K$$ρK modes, the channels to which these two resonances couple most strongly, predicting that these modes peak at different energies and have different widths. These measurements should shed light on the existence of these two $$K_1$$K1 states. In addition, we have gone one step further making a comparison with experimental results of three meson decay channels, letting the vector mesons of our approach decay into pseudoscalars, and we find an overall good agreement with experiment.

scholarly journals Bound-State Solution of s-Wave Klein-Gordon Equation for Woods-Saxon Potential

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Eser Olğar ◽  
Haydar Mutaf
Keyword(s):  
Gordon Equation ◽  
Bound State ◽  
State Solution ◽  
Asymptotic Iteration Method ◽  
Saxon Potential ◽  
Bound State Solution ◽  
S Wave ◽  
Eigenvalues And Eigenfunctions ◽  
Klein Gordon ◽  
Klein Gordon Equation

The bound-state solution of s-wave Klein-Gordon equation is calculated for Woods-Saxon potential by using the asymptotic iteration method (AIM). The energy eigenvalues and eigenfunctions are obtained for the required condition of bound-state solutions.

A new class of Pöschl–Teller potentials with inverse square singularity and their spectra using the asymptotic iteration method

2018 ◽  
Vol 33 (22) ◽  
pp. 1850128 ◽  
Author(s):  
I. A. Assi ◽  
A. J. Sous ◽  
H. Bahlouli
Keyword(s):  
Iteration Method ◽  
Bound States ◽  
Jacobi Polynomials ◽  
Basis Set ◽  
Approximation Schemes ◽  
Asymptotic Iteration Method ◽  
S Wave ◽  
New Class ◽  
New Family ◽  
The Matrix

The aim of this work is to introduce a new family of potentials with inverse square singularity which we called the Pöschl–Teller family of potentials. We enforced the matrix representation of the wave operator to be symmetric and (2k[Formula: see text]+[Formula: see text]1) band-diagonal with respect to a square integrable basis set. This, in principle, is only satisfied for specific potential functions within the used basis set. The basis functions we used here are written in terms of Jacobi polynomials, which is the same basis used in the Tridiagonal Representation Approach (TRA). This yield a more general form of Pöschl–Teller potential that can have many terms which could be beneficial for modeling different physical systems where this potential applies. As an illustration, we have studied a specific new five-parameter potential that belongs to this new family and calculated the bound states for both s-wave and l-wave cases using the Asymptotic Iteration Method (AIM). Along the way, we have introduced new approximation schemes to deal with the l-wave centrifugal potential within the AIM at different approximation orders.

scholarly journals Nuclear Level Density Parameters ofPb203-209andBi206-210Deformed Target Isotopes Used on Accelerator-Driven Systems in Collective Excitation Modes

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Şeref Okuducu ◽  
Nisa N. Aktı ◽  
Sabahattin Akbaş ◽  
M. Orhan Kansu
Keyword(s):  
Collective Excitation ◽  
Level Density ◽  
Neutron Resonance ◽  
Nuclear Level Density ◽  
S Wave ◽  
Nuclear Level ◽  
Driven Systems ◽  
Resonance Data ◽  
Accelerator Driven Systems ◽  
Good Agreement

The nuclear level density parameters of some deformed isotopes of target nuclei (Pb, Bi) used on the accelerator-driven subcritical systems (ADSs) have been calculated taking into consideration different collective excitation modes of observed nuclear spectra near the neutron binding energy. The method used in the present work assumes equidistant spacing of the collective coupled state bands of the considered isotopes. The present calculated results for different collective excitation bands have been compared with the compiled values from the literature for s-wave neutron resonance data, and good agreement was found.

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