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 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.

Application of the exact quantization rule for some noncentral separable potentials

2008 ◽  
Vol 86 (9) ◽  
pp. 1083-1089 ◽  
Author(s):  
Y Kasri ◽  
L Chetouani
Keyword(s):  
Energy Spectrum ◽  
Quantization Rule ◽  
Exact Quantization Rule ◽  
Separable Potentials ◽  
03.65 Ge

The energy spectrum of some noncentral separable potentials are obtained using the exact quantization rule in r and θ dimensions. The results are consistent with those obtained by other methods. PACS Nos.: 03.65.Ca, 03.65.Ge

EXACTLY SOLUBLE MATRIX MODELS

1992 ◽  
Vol 07 (03) ◽  
pp. 251-257
Author(s):  
R. RAJU VISWANATHAN
Keyword(s):  
Exact Solution ◽  
Energy Spectrum ◽  
Matrix Models ◽  
Morse Potential ◽  
Continuum Limit ◽  
Scaling Behavior ◽  
Quantum Corrections ◽  
One Dimensional ◽  
Dimensional Matrix ◽  
The Continuum

We study examples of one-dimensional matrix models whose potentials possess an energy spectrum that can be explicitly determined. This allows for an exact solution in the continuum limit. Specifically, step-like potentials and the Morse potential are considered. The step-like potentials show no scaling behavior and the Morse potential (which corresponds to a γ=−1 model) has the interesting feature that there are no quantum corrections to the scaling behavior in the continuum limit.

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