Explicit solutions for N-dimensional Schrödinger equations with position-dependent mass

Gönül, B.; Koçak, Mehmet Çetin

doi:10.1063/1.2354333

Cited by 16 publications

(6 citation statements)

References 29 publications

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“…According to recent contributions [70,440,441], it is shown that the positiondependent effective mass Schrödinger equation with physical potentials is given by Based on the following formula…”

Section: Formalismmentioning

confidence: 99%

“…Except for these, the higher dimensional Schrödinger equation are also concerned with the following scattered fields such as the position and momentum information entropies of the D-dimensional harmonic oscillator and hydrogen atom [58], the Fermi pseudo-potential in arbitrary dimensions [59], the uncertainty relation for Fisher information of D-dimensional single-particle systems with central po-tentials [60], the dimensional expansion for the Ising limit of quantum field theory [61], the scalar Casimir effect for an N -dimensional sphere [62], the multidimensional extension of a WKB improvement for the spherical quantum billiard zeta functions [63], the study of bound states in continuous D dimensions [64], the suppersymmetry and relationship between a class of singular potentials in arbitrary dimensions [65], the bound states and resonances for "sombrero" potential in arbitrary dimensions [66], the renormalization of the inverse squared potential in D dimensions [67], the generalized coherent states for the d-dimensional Coulomb problem [68], the quantum particles trapped in a position-dependent mass barrier [69,70], the harmonic oscillator in arbitrary dimensions with minimal length uncertainty relations [71], the stable hydrogen atom in higher dimensions [72], the relation between dimension and angular momentum for radially symmetric potential in Ddimensional space [73], the D-dimensional hydrogenic systems in position and momentum spaces [74], the first-order intertwining operators and position-dependent mass Schrödinger equation in d dimensions [75], intertwined isospectral potentials in arbitrary dimensions [76], convergent iterative solutions for a sombrero-shaped potential in any space dimension and arbitrary angular momentum [77].…”

Section: Introduction 1 Basic Reviewmentioning

confidence: 99%

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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: Formalismmentioning

confidence: 99%

Section: Introduction 1 Basic Reviewmentioning

confidence: 99%

Wave Equations in Higher Dimensions

Dong

2011

224

153

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“…Although mostly one-dimensional equations have been considered up to now, several works have recently paid attention to d-dimensional problems [7,17,18,19,20,21,22]. In [7] (henceforth referred to as I and whose equations will be quoted by their number preceded by I), we have analyzed d-dimensional PDM Schrödinger equations in the framework of first-order intertwining operators and shown that with a pair (H, H 1 ) of intertwined Hamiltonians we can associate another pair (R, R 1 ) of second-order partial differential operators related to the same intertwining operator and such that H (resp.…”

Section: Introductionmentioning

confidence: 99%

Quadratic Algebra Approach to an Exactly Solvable Position-Dependent Mass Schrödinger Equation in Two Dimensions

Quesne¹

2007

SIGMA

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Abstract. An exactly solvable position-dependent mass Schrödinger equation in two dimensions, depicting a particle moving in a semi-infinite layer, is re-examined in the light of recent theories describing superintegrable two-dimensional systems with integrals of motion that are quadratic functions of the momenta. To get the energy spectrum a quadratic algebra approach is used together with a realization in terms of deformed parafermionic oscillator operators. In this process, the importance of supplementing algebraic considerations with a proper treatment of boundary conditions for selecting physical wavefunctions is stressed. Some new results for matrix elements are derived. This example emphasizes the interest of a quadratic algebra approach to position-dependent mass Schrödinger equations.

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“…Oyewumi et al [19] studied the N-dimensional Pseudoharmonic oscillator. Gönül and Koçak [20] investigated explicit solutions for N-dimensional Schrödinger equations with position-dependent mass. The N-dimensional Kratzer-Fues potential was discussed by Oyewumi [21], Ikhdair and Sever [22], studied the modi-fied Kratzer-Fues potential plus the ring shape potential in D-dimensions while Dong [23], reviewed the wave equations in higher dimensions.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Eigensolutions of the N-dimensional Schrödinger equation interacting with Varshni-Hulthén potential model

2021

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Analytical solutions of the N-dimensional Schrödinger equation for the newly proposed Varshni-Hulthén potential are obtained within the framework of Nikiforov-Uvarov method by using Greene-Aldrich approximation scheme to the centrifugal barrier. The numerical energy eigenvalues and the corresponding normalized eigenfunctions are obtained in terms of Jacobi polynomials. Special cases of the potential are equally studied and their numerical energy eigenvalues are in agreement with those obtained previously with other methods. However, the behavior of the energy for the ground state and several excited states is illustrated graphically.

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Explicit solutions for N-dimensional Schrödinger equations with position-dependent mass

Cited by 16 publications

References 29 publications

Wave Equations in Higher Dimensions

Wave Equations in Higher Dimensions

Quadratic Algebra Approach to an Exactly Solvable Position-Dependent Mass Schrödinger Equation in Two Dimensions

Eigensolutions of the N-dimensional Schrödinger equation interacting with Varshni-Hulthén potential model

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