Analytical approximations to the solutions of the Manning–Rosen potential with centrifugal term

Qin, Wen; Dong, Shi‐Hai

doi:10.1016/j.physleta.2007.03.057

Cited by 224 publications

(107 citation statements)

References 12 publications

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“…Finally, we shall apply the proper quantization rule to generate the exact solutions of the Manning-Rosen effective potential [387][388][389][390] …”

Section: Energy Spectra For the Manning-rosen Effective Potentialmentioning

confidence: 99%

Wave Equations in Higher Dimensions

Dong

2011

Self Cite

224

153

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No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. PrefaceThis work will introduce the wave equations in higher dimensions at an advanced level addressing students of physics, mathematics and chemistry. The aim is to put the mathematical and physical concepts and techniques like the wave equations, group theory, generalized hypervirial theorem, the Levinson theorem, exact and proper quantization rules related to the higher dimensions at the reader's disposal. For this purpose, we attempt to provide a comprehensive description of the wave equations including the non-relativistic Schrödinger equation, relativistic Dirac and Klein-Gordon equations in higher dimensions and their wide applications in quantum mechanics which complements the traditional coverage found in the existing quantum mechanics textbooks. Related to this field are the quantum mechanics and group theory. In fact, the author's driving force has been his desire to provide a comprehensive review volume that includes some new and significant results about the wave equations in higher dimensions drawn from the teaching and research experience of the author since the literature is inundated with scattered articles in this field and to pave the reader's way into this territory as rapidly as possible. We have made the effort to present the clear and understandable derivations and include the necessary mathematical steps so that the intelligent and diligent reader is able to follow the text with relative ease, in particular, when mathematically difficult material is presented. The author also embraces enthusiastically the potential of the LaTeX typesetting language to enrich the presentation of the formulas as to make the logical pattern behind the mathematics more transparent. In addition, any suggestions and criticism to improve the text are most welcome. It should be pointed out that the main effort to follow the text and master the material is left to the reader even though this book makes an effort to serve the reader as much as was possible for the author. This book starts out in Chap. 1 with a comprehensive review for the wave equations in higher dimensions and builds on this to introduce in Chap. 2 the fundamental theory about the SO(N ) group to be used in the successive Chaps. 3-5 including the non-relativistic Schrödinger equation, relativistic Dirac and Klein-Gordon equations. As important applications in non-relativistic quantum mechanics, from Chap. 6 to Chap. 12, we shall apply the theories proposed in Part II to study some vii viii Preface important quantum systems such as the harmonic oscillator, Coulomb potential, the Levinson theorem, generalized hypervirial theorem, exact and proper...

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“…Finally, we shall apply the proper quantization rule to generate the exact solutions of the Manning-Rosen effective potential [387][388][389][390] …”

Section: Energy Spectra For the Manning-rosen Effective Potentialmentioning

confidence: 99%

Wave Equations in Higher Dimensions

Dong

2011

Self Cite

224

153

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“…To solve Eq. (165), we can think about an approximation regarding with the centrifugal term as follows (Greene & Aldrich, 1976;Qiang & Dong, 2007) ℓ(ℓ + 1) r 2 ≈ ℓ(ℓ + 1)e −r/κ κ 2 (1 − e −r/κ ) 2 .…”

Section: Hulthen Potentialmentioning

confidence: 99%

Application of the Nikiforov-Uvarov Method in Quantum Mechanics

Berkdemir¹

2012

Theoretical Concepts of Quantum Mechanics

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“…2 In terms of the wave functions for diatomic molecules, one can calculate the transition dipole matrix elements. [3][4][5] Some authors have investigated analytical solutions of the Schrödinger equation with typical diatomic molecule potential models, such as the Morse potential, 6 Deng−Fan potential, 7-10 Rosen−Morse potential, 11,12 Manning−Rosen potential, [13][14][15][16][17] Wei potential, 18 and Schiöberg potential. 19 In 1932, Rosen and Morse 20 proposed a potential energy function for polyatomic molecules: (1) U RM (r) ϭ B tanh (r/d) Ϫ C sech 2 (r/d)…”

Section: Introductionmentioning

confidence: 99%

Molecular energies of the improved Rosen−Morse potential energy model

2014

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We solve the Schrödinger equation with the improved Rosen−Morse empirical potential energy model. The rotationvibrational energy spectra and the unnormalized radial wave functions have been obtained. The interaction potential energy curves for the 3 3 ⌺ g + state of the Cs 2 molecule and the 5 1 ⌬ g state of the Na 2 molecule are modeled by employing the improved Rosen−Morse potential and the Morse potential. Favourable agreement for the improved Rosen−Morse potential is found in comparing with the Rydberg−Klein−Rees potential. The vibrational energy levels predicted by using the improved Rosen−Morse potential for the 3 3 ⌺ g + state of Cs 2 and the 5 1 ⌬ g state of Na 2 are in better agreement with the Rydberg−Klein−Rees data than the predictions of the Morse potential.

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Analytical approximations to the solutions of the Manning–Rosen potential with centrifugal term

Cited by 224 publications

References 12 publications

Wave Equations in Higher Dimensions

Wave Equations in Higher Dimensions

Application of the Nikiforov-Uvarov Method in Quantum Mechanics

Molecular energies of the improved Rosen−Morse potential energy model

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