Improved shifted 1/<i>N</i>expansion

Christiansen, H. R.; Epele, LN; Fanchiotti, H.; Canal, C.A. Garcia

doi:10.1103/physreva.40.1760

Cited by 25 publications

(14 citation statements)

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“…Table IV presents the calculated eigenvalues of some representative states with n ≤ 6 at selected values of the screening parameter (weak and strong screenings in the left and right respectively). Lower states have been examined by many methods; e.g., Rayleigh-Schrödinger perturbation expansion [21], variational methods [6,15,16], Padé approximations [20], shifted 1/N expansions [22,25], numerical calculations through direct integration of the SE [30] or by the Ritz method [31], etc. Other works include [12,33].…”

Section: Resultsmentioning

confidence: 99%

“…Many formally attractive and efficient formalisms have been proposed for accurate determination of the eigenvalues, eigenfunctions as well as for the values of the critical screening parameters differing in complexity, accuracy and efficiency. The most notable of these are the variational calculations employing a multitude of basis functions [14][15][16][17][18]12], combined Padé approximation and perturbation theory [19][20][21], shifted 1/N approximation along with many of its variants [22][23][24][25][26][27], dynamical-group approach [28], supersymmetric quantum mechanics [29], numerical calculations [30][31]18] and other works [32][33].…”

Section: Introductionmentioning

confidence: 99%

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The generalized pseudospectral approach to the bound states of the Hulthén and the Yukawa potentials

Roy

2005

Pramana - J Phys

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The generalized pseudospectral method is employed to calculate the bound states of Hulthén and Yukawa potentials in quantum mechanics, with special emphases on higher excited states and stronger couplings. Accurate energy eigenvalues, expectation values and radial probability densities are obtained through a nonuniform and optimal spatial discretization of the radial Schrödinger equation. Results accurate up to thirteen to fourteen significant figures are reported for all the 55 eigenstates of both these potentials with n ≤10 for arbitrary values of the screening parameters covering a wide range of interaction. Furthermore, excited states as high as up to n = 17 have been computed with good accuracy for both these potentials. Excellent agreement with the available literature data has been observed in all cases. The n > 6 states of Yukawa potential has been considerably improved over all other existing results currently available, while the same for Hulthén potential are reported here for the first time. Excepting the 1s and 2s states of Yukawa potential, the present method surpasses in accuracy all other existing results in the stronger coupling region for all other states of both these systems. This offers a simple and efficient scheme for the accurate calculation of these and other screened Coulomb potentials. * Electronic address: akroy@unb.ca

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The generalized pseudospectral approach to the bound states of the Hulthén and the Yukawa potentials

Roy

2005

Pramana - J Phys

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“…On the contrary, the study on this field has revived and attracted much attention to many authors in 1980s, e.g., the eigenvalues of the Schrödinger equation for spherically symmetric states for various types of potentials in N dimensions by using perturbative and non-perturbative methods [42], the 1/N expansion technique for the Schrödinger equation [43][44][45][46][47][48][49][50][51][52][53], the generalized D-dimensional oscillator [54]. On the contrary, the study on this field has revived and attracted much attention to many authors in 1980s, e.g., the eigenvalues of the Schrödinger equation for spherically symmetric states for various types of potentials in N dimensions by using perturbative and non-perturbative methods [42], the 1/N expansion technique for the Schrödinger equation [43][44][45][46][47][48][49][50][51][52][53], the generalized D-dimensional oscillator [54].…”

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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“…As stated before in [59][60][61][62][63][64][65][66][67][68][69][70][71][72][73], for any fixed n the computed energies become more convergent as l increases. This is expected since the expansion parameter 1/N or 1/k becomes smaller as l becomes larger since the parameter k is proportional to n and appears in the denominator in higher-order correction.…”

Section: +018mentioning

confidence: 62%

“…and to solve for the shifting parameter a, the next contribution to the energy eigenvalue E 1 is chosen to vanish [72,73] so that the second-and third-order corrections are very small compared with the leading term contribution. The energy states are calculated by considering the leading term E 0 and the second-order and third-order corrections, it implies the shifting parameter…”

Section: +018mentioning

confidence: 99%

CALCULATION OF THE B_c LEPTONIC DECAY CONSTANT USING THE SHIFTED N-EXPANSION METHOD

Ikhdair

Sever

2006

Int. J. Mod. Phys. A

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We give a review and present a comprehensive calculation for the leptonic constant f Bc of the low-lying pseudoscalar and vector states of B c -meson in the framework of static and QCD-motivated nonrelativistic potential models taking into account the one-loop and two-loop QCD corrections in the short distance coefficient that governs the leptonic constant of B c quarkonium system. Further, we use the scaling relation to predict the leptonic constant of the nS-states of the bc system. Our results are compared with other models to gauge the reliability of the predictions and point out differences.

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Improved shifted 1/Nexpansion

Cited by 25 publications

References 10 publications

The generalized pseudospectral approach to the bound states of the Hulthén and the Yukawa potentials

The generalized pseudospectral approach to the bound states of the Hulthén and the Yukawa potentials

Wave Equations in Higher Dimensions

CALCULATION OF THE B_c LEPTONIC DECAY CONSTANT USING THE SHIFTED N-EXPANSION METHOD

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Improved shifted 1/Nexpansion

Cited by 25 publications

References 10 publications

The generalized pseudospectral approach to the bound states of the Hulthén and the Yukawa potentials

The generalized pseudospectral approach to the bound states of the Hulthén and the Yukawa potentials

Wave Equations in Higher Dimensions

CALCULATION OF THE Bc LEPTONIC DECAY CONSTANT USING THE SHIFTED N-EXPANSION METHOD

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CALCULATION OF THE B_c LEPTONIC DECAY CONSTANT USING THE SHIFTED N-EXPANSION METHOD