Modified Unequal Mixture Scalar Vector Hulthén–Yukawa Potentials Model as a Quark–Antiquark Interaction and Neutral Atoms via Relativistic Treatment Using the Improved Approximation of the Centrifugal Term and Bopp’s Shift Method

2020 ◽  
Vol 61 (3) ◽  
Author(s):  
Abdelmadjid Maireche
2020 ◽  
Vol 29 (09) ◽  
pp. 2050067
Author(s):  
E. Yazdankish

The Yukawa potential has an important and significant rule in some branches of physics such as nuclear, plasma and solid state. However, there is no analytical solution for Schrödinger equation with this potential without approximation, therefore, other ways, such as numerical, perturbation, variation and so on, are taken to deal with this potential. In this work, the variation principle is taken to obtain some of its energy eigenvalues. In the arbitrary [Formula: see text]-state, the Yukawa potentials with centrifugal term are taken together as effective potential and then by choosing the wave functions of the Hulthen potential as trial function which are obtained in this work from the Nikiforov–Uvarov method, and then by applying the variation principle, the energy eigenvalues are obtained. After that, the result is compared with the former numerical result. The comparison shows excellent agreement between our result and the former numerical ones.


1996 ◽  
Author(s):  
David E. Pritchard ◽  
Wolfgang Ketterle
Keyword(s):  

Author(s):  
Richard R. Freeman ◽  
James A. King ◽  
Gregory P. Lafyatis

Electromagnetic Radiation is a graduate level book on classical electrodynamics with a strong emphasis on radiation. This book is meant to quickly and efficiently introduce students to the electromagnetic radiation science essential to a practicing physicist. While a major focus is on light and its interactions, topics in radio frequency radiation, x-rays, and beyond are also treated. Special emphasis is placed on applications, with many exercises and homework problems. The format of the book is designed to convey the basic concepts of a topic in the main central text in the book in a mathematically rigorous manner, but with detailed derivations routinely relegated to the accompanying side notes or end of chapter “Discussions.” The book is composed of four parts: Part I is a review of basic E&M, and assumes the reader has a had a good upper division undergraduate course, and while it offers a concise review of topics covered in such a course, it does not treat any given topic in detail; specifically electro- and magnetostatics. Part II addresses the origins of radiation in terms of time variations of charge and current densities within the source, and presents Jefimenko’s field equations as derived from retarded potentials. Part III introduces special relativity and its deep connection to Maxwell’s equations, together with an introduction to relativistic field theory, as well as the relativistic treatment of radiation from an arbitrarily accelerating charge. A highlight of this part is a chapter on the still partially unresolved problem of radiation reaction on an accelerating charge. Part IV treats the practical problems of electromagnetic radiation interacting with matter, with chapters on energy transport, scattering, diffraction and finally an illuminating, application-oriented treatment of fields in confined environments.


2008 ◽  
Vol 78 (5) ◽  
Author(s):  
Zygmunt Patyk ◽  
Hans Geissel ◽  
Yuri A. Litvinov ◽  
Agatino Musumarra ◽  
Chiara Nociforo
Keyword(s):  

Author(s):  
Hirotaka Takahashi ◽  
Katsuhiro Matsuda ◽  
Yasushi Tomita ◽  
Takashi Oda ◽  
Eri Isozaki

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