Two-center matrix elements for Kratzer oscillators

Bastida, Adolfo; Zúñiga, José; Alacid, Mercedes; Requena, A.; Hidalgo, Antonio

doi:10.1063/1.458820

Cited by 15 publications

(7 citation statements)

References 14 publications

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“…Recently, we have studied the Klein-Gordon equation case [322]. Moreover, the two-center matrix elements and the recurrence relations for the Kratzer oscillator were investigated [323], which has also been derived by means of a hypervirial-like theorem procedure [324]. Moreover, the two-center matrix elements and the recurrence relations for the Kratzer oscillator were investigated [323], which has also been derived by means of a hypervirial-like theorem procedure [324].…”

Section: Introductionmentioning

confidence: 99%

Wave Equations in Higher Dimensions

Dong

2011

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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Section: Introductionmentioning

confidence: 99%

Wave Equations in Higher Dimensions

Dong

2011

224

153

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“…Another type of noncentral potentials is the ring-shaped Kratzer potential, which is a combination of a Coulomb potential plus an inverse square potential plus a noncentral angular part [31,32]. The Kratzer potential has been used to describe the vibrational-rotational motion of isolated diatomic molecules [33] and has a mixed-energy spectrum containing both bound and scattering states with bound-states have been widely used in molecular spectroscopy [34]. The ring-shaped Kratzer potential consists of radial and angular-dependent potentials and is useful in studying ring-shaped molecules [22].…”

Section: Introductionmentioning

confidence: 99%

“…The Kratzer potential has been used to describe the vibrational-rotational motion of isolated diatomic molecules [50] and has a mixed-energy spectrum containing both bound and scattering states, with boundstates have been widely used in molecular spectroscopy [51]. The ring-shaped Kratzer potential consists of radial and angle-dependent potentials and is useful in studying ring-shaped molecules [37].…”

Section: Introductionmentioning

confidence: 99%

Relativistic solution in D-dimensions to a spin-zero particle for equal scalar and vector ring-shaped Kratzer potential

Ikhdair¹,

Sever

2008

Open Physics

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“…There has been a long history of attempts to calculate the matrix elements and the recurrence relations among them for some important wavefunctions such as the Coulomblike potential, harmonic oscillator and Kratzer oscillator and so on [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] because of their wide applications in physics 3 . For example, in order to simplify the calculations of the matrix elements for the Coulomb-like potential, some methods such as the relationship among the Laguerre polynomials, Dirac's 'q-number', the generalized hypergeometric function, the group theoretical approach, the Schrödinger radial ladder operators, the hypervirial theorem and the various sum rules were used [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Generalized hypervirial and Blanchard's recurrence relations for radial matrix elements

Dong

Chen

Lozada‐Cassou

2005

J. Phys. B: At. Mol. Opt. Phys.

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Based on the Hamiltonian identity, we propose a generalized expression of the second hypervirial for an arbitrary central potential wavefunction in arbitrary dimensions D. We demonstrate that the new proposed second hypervirial formula is very powerful in deriving the general Blanchard's and Kramers' recurrence relations among the radial matrix elements. As their useful and important applications, we derive all general Blanchard's and Kramers' recurrence relations and some identities for the Coulomb-like potential, harmonic oscillator and Kratzer oscillator. The recurrence relation and identity between the exponential functions and the powers of the radial function are established for the Morse potential. The corresponding general Blanchard's and Kramers' recurrence relations in 2D are also briefly studied.

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Two-center matrix elements for Kratzer oscillators

Cited by 15 publications

References 14 publications

Wave Equations in Higher Dimensions

Wave Equations in Higher Dimensions

Relativistic solution in D-dimensions to a spin-zero particle for equal scalar and vector ring-shaped Kratzer potential

Generalized hypervirial and Blanchard's recurrence relations for radial matrix elements

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