scholarly journals Energy States of Some Diatomaic Molecules: The Exact Quantisation Rule Approach

2015 ◽  
Vol 70 (2) ◽  
pp. 85-90 ◽  
Author(s):  
Babatunde J. Falaye ◽  
Sameer M. Ikhdair ◽  
Majid Hamzavi
Keyword(s):  
Hypergeometric Functions ◽  
Vibrational Energy ◽  
Energy Levels ◽  
Wave Functions ◽  
Energy Eigenvalues ◽  
Molecular Potential ◽  
Approximate Analytical Solutions ◽  
Rule Approach ◽  
Radial Schrödinger Equation ◽  
Good Agreement

AbstractIn this study, we obtain the approximate analytical solutions of the radial Schrödinger equation for the Deng–Fan diatomic molecular potential by using the exact quantisation rule approach. The wave functions were expressed by hypergeometric functions via the functional analysis approach. An extension to the rotational–vibrational energy eigenvalues of some diatomic molecules is also presented. It is shown that the calculated energy levels are in good agreement with those obtained previously (Enℓ–D; shifted Deng–Fan).

Approximate Ro-Vibrational Spectrum of the Modified Rosen–Morse Molecular Potential Using the Nikiforov–Uvarov Method

2013 ◽  
Vol 68 (6-7) ◽  
pp. 427-432 ◽  
Author(s):  
Ali Akbar Rajabi ◽  
Majid Hamzavi
Keyword(s):  
Vibrational Spectrum ◽  
Schrodinger Equation ◽  
Approximation Scheme ◽  
Centrifugal Term ◽  
Energy Eigenvalues ◽  
Molecular Potential ◽  
Radial Schrödinger Equation ◽  
Uvarov Method ◽  
Nu Method ◽  
Good Agreement

By using the Nikiforov-Uvarov (NU) method and a new approximation scheme to the centrifugal term, we obtained the solutions of the radial Schrödinger equation (SE) for the modified Rosen- Morse (mRM) potential. In this paper, we get the approximate energy eigenvalues and show that the results are in good agreement with those obtained before. Eigenfunctions are also presented for completeness.

scholarly journals Bound-state solutions and thermal properties of the modified Tietz–Hua potential

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
C. A. Onate ◽  
M. C. Onyeaju ◽  
E. Omugbe ◽  
I. B. Okon ◽  
O. E. Osafile
Keyword(s):  
Thermal Properties ◽  
Vibrational Energy ◽  
Approximate Solutions ◽  
Bound State ◽  
Effect Of Temperature ◽  
Energy Eigenvalues ◽  
Radial Schrödinger Equation ◽  
Vibrational Energies ◽  
Good Agreement ◽  
Supersymmetric Approach

AbstractAn approximate solutions of the radial Schrödinger equation was obtained under a modified Tietz–Hua potential via supersymmetric approach. The effect of the modified parameter and optimization parameter respectively on energy eigenvalues were graphically and numerically examined. The comparison of the energy eigenvalues of modified Tietz–Hua potential and the actual Tietz–Hua potential were examined. The ro-vibrational energy of four molecules were also presented numerically. The thermal properties of the modified Tietz–Hua potential were calculated and the effect of temperature on each of the thermal property were examined under hydrogen fluoride, hydrogen molecule and carbon (ii) oxide. The study reveals that for a very small value of the modified parameter, the energy eigenvalues of the modified Tietz–Hua potential and that of the actual Tietz–Hua potential are equivalent. Finally, the vibrational energies for Cesium molecule was calculated and compared with the observed value. The calculated results were found to be in good agreement with the observed value.

Approximate Analytical Solutions of the Perturbed Yukawa Potential with Centrifugal Barrier

2013 ◽  
Vol 68 (6-7) ◽  
pp. 454-460 ◽  
Author(s):  
Ali Akbar Rajabi ◽  
Majid Hamzavi
Keyword(s):  
Analytical Solutions ◽  
Yukawa Potential ◽  
Energy Levels ◽  
Centrifugal Barrier ◽  
Energy Eigenvalues ◽  
Approximate Analytical Solutions ◽  
Screening Parameter ◽  
Radial Schrödinger Equation ◽  
Type Potential ◽  
Coulomb Potentials

By using the generalized parametric Nikiforov-Uvarov (NU) method, we have obtained the approximate analytical solutions of the radial Schrödinger equation for a perturbed Yukawa potential. The energy eigenvalues and corresponding eigenfunctions are calculated in closed forms. Some numerical results are presented and compared with the standard Yukawa potential. Further, we found the energy levels of the familiar Mie-type potential when the screening parameter of the perturbed Yukawa potential goes to zero, and finally, standard Yukawa and Coulomb potentials are discussed.

scholarly journals Algebraic Approach to Exact Solution of the (2 + 1)-Dimensional Dirac Oscillator in the Noncommutative Phase Space

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
H. Panahi ◽  
A. Savadi
Keyword(s):  
Exact Solution ◽  
Phase Space ◽  
Algebraic Approach ◽  
Wave Functions ◽  
Dirac Oscillator ◽  
Noncommutative Phase Space ◽  
Energy Eigenvalues ◽  
Good Agreement

We study the (2 + 1)-dimensional Dirac oscillator in the noncommutative phase space and the energy eigenvalues and the corresponding wave functions of the system are obtained through the sl(2) algebraization. It is shown that the results are in good agreement with those obtained previously via a different method.

Ab Initio Calculations of Vibrational Energy Levels and Transition Dipole Moments of CO2 Molecules

2008 ◽  
Author(s):  
Zhi Liang ◽  
Hai-Lung Tsai
Keyword(s):  
Ab Initio ◽  
Vibrational Energy ◽  
Molecular Spectroscopy ◽  
Dipole Moments ◽  
Energy Levels ◽  
Wave Functions ◽  
Molecular Vibration ◽  
Transition Dipole ◽  
Transition Dipole Moments ◽  
Vibrational Energy Levels

Ab initio MD simulation of laser-matter interactions is a hot area in the study of the mechanisms of photo-dissociation, photo-ionization and laser induced chemical reactions. The major problems in the study of laser-molecule interactions are to determine the energies and wave functions of molecular vibration states and the molecular transition dipole moments. An efficient method is presented to calculate the intramolecular potential energies and electrical dipole moments of CO2 molecules at the electronic ground state by solving the Kohn-Sham (KS) equation for a total of 101,992 nuclear configurations. The Projector-Augmented Wave (PAW) exchange-correlation potential functionals and Plane Wave (PW) basis functions were used in solving the KS equation. The calculated intra-molecular potential function was then included in the pure vibrational Schro¨dinger equation to determine the vibrational energy eigen values and eigen functions. The vibrational wave functions combined with the calculated dipole moment function were used to determine the transition dipole moments. The calculated results have a good agreement with experimental values. These results can be further used to determinations of molecular spectroscopy and laser absorption coefficients.

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 Pseudospin and Spin Symmetric Solutions of the Dirac Equation: Hellmann Potential,Wei–Hua Potential, Varshni Potential

2014 ◽  
Vol 69 (3-4) ◽  
pp. 163-172 ◽  
Author(s):  
Altuğ Arda ◽  
Ramazan Sever
Keyword(s):  
Dirac Equation ◽  
Analytical Solutions ◽  
Energy Eigenvalue ◽  
Wave Functions ◽  
K Value ◽  
Energy Eigenvalues ◽  
Approximate Analytical Solutions ◽  
Hellmann Potential ◽  
Uvarov Method ◽  
Spinor Wave

Approximate analytical solutions of the Dirac equation are obtained for the Hellmann potential, the Wei-Hua potential, and the Varshni potential with any k-value for the cases having the Dirac equation pseudospin and spin symmetries. Closed forms of the energy eigenvalue equations and the spinor wave functions are obtained by using the Nikiforov-Uvarov method and some tables are given to see the dependence of the energy eigenvalues on different quantum number pairs (n;κ).

scholarly journals The bound state solutions of the D-dimensional Schrödinger equation for the Woods–Saxon potential

2016 ◽  
Vol 25 (01) ◽  
pp. 1650002 ◽  
Author(s):  
V. H. Badalov
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound State ◽  
Wave Functions ◽  
Saxon Potential ◽  
Radial Wave ◽  
Energy Eigenvalues ◽  
Quantum Numbers ◽  
Radial Schrödinger Equation ◽  
Pekeris Approximation

In this work, the analytical solutions of the [Formula: see text]-dimensional radial Schrödinger equation are studied in great detail for the Wood–Saxon potential by taking advantage of the Pekeris approximation. Within a novel improved scheme to surmount centrifugal term, the energy eigenvalues and corresponding radial wave functions are found for any angular momentum case within the context of the Nikiforov–Uvarov (NU) and Supersymmetric quantum mechanics (SUSYQM) methods. In this way, based on these methods, the same expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformed each other is demonstrated. In addition, a finite number energy spectrum depending on the depth of the potential [Formula: see text], the radial [Formula: see text] and orbital [Formula: see text] quantum numbers and parameters [Formula: see text] are defined as well.

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