Arbitrary l-state solutions of the rotating Morse potential through the exact quantization rule method

2007 ◽  
Vol 363 (3) ◽  
pp. 169-176 ◽  
Author(s):  
Wen-Chao Qiang ◽  
Shi-Hai Dong
Keyword(s):  
Morse Potential ◽  
Quantization Rule ◽  
Exact Quantization Rule ◽  
Rule Method

scholarly journals Exact quantization rule and the invariant

2006 ◽  
Vol 55 (4) ◽  
pp. 1571
Author(s):  
Ma Zhong-Qi ◽  
Xu Bo-Wei
Keyword(s):  
Quantization Rule ◽  
Exact Quantization Rule

Energy spectrum of the trigonometric Rosen–Morse potential using an improved quantization rule

2007 ◽  
Vol 371 (3) ◽  
pp. 180-184 ◽  
Author(s):  
Zhong-Qi Ma ◽  
A. Gonzalez-Cisneros ◽  
Bo-Wei Xu ◽  
Shi-Hai Dong
Keyword(s):  
Energy Spectrum ◽  
Morse Potential ◽  
Quantization Rule

scholarly journals Approximate analytical solutions for arbitrary l-state of the Hulthén potential with an improved approximation of the centrifugal term

2011 ◽  
Vol 9 (4) ◽  
pp. 737-742 ◽  
Author(s):  
Jerzy Stanek
Keyword(s):  
Bound State ◽  
Centrifugal Term ◽  
Approximate Methods ◽  
Quantization Rule ◽  
Hulthén Potential ◽  
Hulthen Potential ◽  
Approximate Analytical Solutions ◽  
Exact Quantization Rule ◽  
Screening Parameter ◽  
Uvarov Method

AbstractAn approximate analytical solution of the radial Schrödinger equation for the generalized Hulthén potential is obtained by applying an improved approximation of the centrifugal term. The bound state energy eigenvalues and the normalized eigenfunctions are given in terms of hypergeometric polynomials. The results for arbitrary quantum numbers n r and l with different values of the screening parameter δ are compared with those obtained by the numerical method, asymptotic iteration, the Nikiforov-Uvarov method, the exact quantization rule, and variational methods. The results obtained by the method proposed in this work are in a good agreement with those obtained by other approximate methods.

scholarly journals A Theoretical Study on Vibrational Energies of Molecular Hydrogen and Its Isotopes Using a Semi-classical Approximation

2021 ◽  
Vol 21 (3) ◽  
pp. 725
Author(s):  
Redi Kristian Pingak ◽  
Albert Zicko Johannes ◽  
Fidelis Nitti ◽  
Meksianis Zadrak Ndii
Keyword(s):  
Molecular Hydrogen ◽  
Morse Potential ◽  
Theoretical Study ◽  
Potential Functions ◽  
Percentage Error ◽  
Quantization Rule ◽  
Classical Approximation ◽  
Vibrational Energies ◽  
Rosen Potential ◽  
Better Than

This study aims to apply a semi-classical approach using some analytically solvable potential functions to accurately compute the first ten pure vibrational energies of molecular hydrogen (H2) and its isotopes in their ground electronic states. This study also aims at comparing the accuracy of the potential functions within the framework of the semi-classical approximation. The performance of the approximation was investigated as a function of the molecular mass. In this approximation, the nuclei were assumed to move in a classical potential. The Bohr-Sommerfeld quantization rule was then applied to calculate the vibrational energies of the molecules numerically. The results indicated that the first vibrational transition frequencies (v1ß0) of all hydrogen isotopes were consistent with the experimental ones, with a minimum percentage error of 0.02% for ditritium (T2) molecule using the Modified-Rosen-Morse potential. It was also demonstrated that, in general, the Rosen-Morse and the Modified-Rosen-Morse potential functions were better in terms of calculating the vibrational energies of the molecules than Morse potential. Interestingly, the Morse potential was found to be better than the Manning-Rosen potential. Finally, the semi-classical approximation was found to perform better for heavier isotopes for all potentials applied in this study.

scholarly journals ROTATIONAL-VIBRATIONAL EIGEN SOLUTIONS OF THE D-DIMENSIONAL SCHRÖDINGER EQUATION FOR THE IMPROVED WEI POTENTIAL

2020 ◽  
Vol 4 (2) ◽  
pp. 269-283
Author(s):  
Edwin Samson Eyube ◽  
Yabwa Dlama ◽  
Umar Wadata
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Goodness Of Fit ◽  
Bound State ◽  
Fit Indices ◽  
Quantization Rule ◽  
Exact Quantization Rule ◽  
Vibrational Energies ◽  
Eigen Solutions ◽  
Tietz Potential

In this present study, we have employed the techniques of exact quantization rule and ansatz solution method to obtain closed form expressions for the rotational-vibrational eigensolutions of the D-dimensional Schrödinger equation for the improved Wei potential, for cases of h′ ≠ 0 and h′ = 0. By using our derived energy equation and choosing arbitrary values of n and ℓ, we have computed the bound state rotational-vibrational energies of CO, H2 and LiH for various quantum states. The mean absolute percentage deviation (MAPD) and the Lippincott criterion ware used as a goodness-of-fit indices to compare our result with the Rydberg-Klein-Rees (RKR) and improved Tietz potential data in the literature. MAPD of 0.2862%, 0.2896% and 0.0662% relative to the RKR data for CO ware obtained. For the improved Wei and Morse potential, our computed energy eigenvalues for CO, H2 and LiH are in excellent agreement with existing results in the literature

EXACT QUANTIZATION RULE AND ITS APPLICATIONS TO PHYSICAL POTENTIALS

2007 ◽  
Vol 16 (01) ◽  
pp. 189-198 ◽  
Author(s):  
SHI-HAI DONG ◽  
D. MORALES ◽  
J. GARCÍA-RAVELO
Keyword(s):  
Harmonic Oscillator ◽  
Analytical Solutions ◽  
Bound States ◽  
Energy Levels ◽  
Present Approach ◽  
Three Dimensions ◽  
One Dimension ◽  
Quantization Rule ◽  
Exact Quantization Rule ◽  
Pseudoharmonic Oscillator

By using the exact quantization rule, we present analytical solutions of the Schrödinger equation for the deformed harmonic oscillator in one dimension, the Kratzer potential and pseudoharmonic oscillator in three dimensions. The energy levels of all the bound states are easily calculated from this quantization rule. The normalized wavefunctions are also obtained. It is found that the present approach can simplify the calculations.

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