Feynman kernel analytical solutions for the deformed hyperbolic barrier potential with application to some diatomic molecules

2021 ◽  
Author(s):  
Mohamed M'Hamed Ezzine ◽  
Mohammed Hachama ◽  
Ahmed Diaf
Keyword(s):  
Energy Spectrum ◽  
Path Integral ◽  
Diatomic Molecules ◽  
Euler Angles ◽  
Centrifugal Term ◽  
Feynman Path Integral ◽  
Integral Formalism ◽  
Feynman Path ◽  
Barrier Potential ◽  
Good Agreement

Abstract In this paper, we derive the `-states energy spectrum of the q-deformed hyperbolic Barrier Potential. Within the Feynman path integral formalism, we propose an appropriate approximation of the centrifugal term. Then, using Euler angles and the isomorphism between S3and SU(1, 1), we convert the radial path integral into a maniable one. The obtained eigenvalues are in very good agreement with the numerical results. In addition, we applied our results to some diatomic molecules and obtained accurate results compared to the experimental (RKR) values.

PATH INTEGRAL APPROACH TO A SINGLE POLYMER CHAIN WITH RANDOM MEDIA

2004 ◽  
Vol 18 (10n11) ◽  
pp. 1465-1478 ◽  
Author(s):  
CH. KUNSOMBAT ◽  
V. SA-YAKANIT
Keyword(s):  
Polymer Chain ◽  
Path Integral ◽  
Random Media ◽  
Feynman Path Integral ◽  
Feynman Path ◽  
Short Range Correlation ◽  
Range Correlation ◽  
End Distance ◽  
Non Local ◽  
The Mean

In this paper we consider the problem of a polymer chain in random media with finite correlation. We show that the mean square end-to-end distance of a polymer chain can be obtained using the Feynman path integral developed by Feynman for treating the polaron problem and successfuly applied to the theory of heavily doped semiconductor. We show that for short-range correlation or the white Gaussian model we derive the results obtained by Edwards and Muthukumar using the replica method and for long-range correlation we obtain the result of Yohannes Shiferaw and Yadin Y. Goldschimidt. The main idea of this paper is to generalize the model proposed by Edwards and Muthukumar for short-range correlation to finite correlation. Instead of using a replica method, we employ the Feynman path integral by modeling the polymer Hamiltonian as a model of non-local quadratic trial Hamiltonian. This non-local trial Hamiltonian is essential as it will reflect the translation invariant of the original Hamiltonian. The calculation is proceeded by considering the differences between the polymer propagator and the trial propagator as the first cumulant approximation. The variational principle is used to find the optimal values of the variational parameters and the mean square end-to-end distance is obtained. Several asymptotic limits are considered and a comparison between this approaches and replica approach will be discussed.

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