Continuation of the Wave Function for Higher Angular Momentum States toDDimensions

Dunn, Martin; Watson, D. K.

doi:10.1006/aphy.1996.0114

Cited by 20 publications

(15 citation statements)

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“…It could be applied to angular momentum states of multi -electron atoms [34][35][36], relativistic and nonrelativistic quark -antiquark models [37], etc.…”

Section: Discussionmentioning

confidence: 99%

Part of theD-dimensional spiked harmonic oscillator spectra

Mustafa

Odeh

2000

J. Phys. A: Math. Gen.

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“…It could be applied to angular momentum states of multi -electron atoms [34][35][36], relativistic and nonrelativistic quark -antiquark models [37], etc.…”

Section: Discussionmentioning

confidence: 99%

Part of theD-dimensional spiked harmonic oscillator spectra

Mustafa

Odeh

2000

J. Phys. A: Math. Gen.

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“…Following the introduction of 'interdimensional degeneracies' [9,10] there have been several reports involving arbitrary d-dimensional analyses covering many branches of chemical physics which have been briefly reviewed in Refs. [11][12][13][14]. It is interesting to note here that the information-theoretical uncertainty-like relationships in terms of the Shannon entropy [15,16] and the Fisher measure [17,18] are also stated in d-dimensional form.…”

Section: B Degeneracy In Spherically Confined D-dimensional Quantum M...mentioning

confidence: 99%

Discrete spectra for confined and unconfined −a/r + br2 potentials in d-dimensions

Hall

Saad

Sen

2011

Journal of Mathematical Physics

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Exact solutions to the d-dimensional Schrödinger equation, d ≥ 2, for Coulomb plus harmonic oscillator potentials V (r) = −a/r + br 2 , b > 0 and a = 0 are obtained. The potential V (r) is considered both in all space, and under the condition of spherical confinement inside an impenetrable spherical box of radius R. With the aid of the asymptotic iteration method, the exact analytic solutions under certain constraints, and general approximate solutions, are obtained. These exhibit the parametric dependence of the eigenenergies on a, b, and R. The wave functions have the simple form of a product of a power function, an exponential function, and a polynomial. In order to achieve our results the question of determining the polynomial solutions of the second-order differential equation

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“…For example, Hosoya investigated the hierarchical structure of the set of atomic orbital wavefunctions of D-dimensional atoms by using the set of their rectangular coordinate expressions [78]. To overcome the difficulty occurred in [79,80], Ma and his coauthors made use of the group theory method [81] to develop a different formalism to separate the D-dimensional rotational degrees of freedom from the internal degrees of freedom. However, their method seems rather complicated.…”

Section: Introduction 1 Basic Reviewmentioning

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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Continuation of the Wave Function for Higher Angular Momentum States toDDimensions

Cited by 20 publications

References 68 publications

Part of theD-dimensional spiked harmonic oscillator spectra

Part of theD-dimensional spiked harmonic oscillator spectra

Discrete spectra for confined and unconfined −a/r + br2 potentials in d-dimensions

Wave Equations in Higher Dimensions

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