Bound states and band structure—A unified treatment through the quantum Hamilton–Jacobi approach

Ranjani, S. Sree; Kapoor, A. K.; Panigrahi, Prasanta K.

doi:10.1016/j.aop.2005.05.004

Cited by 17 publications

(15 citation statements)

References 18 publications

(28 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the other hand, quantum Hamilton-Jacobi (QHJ) formalism has generated much interest [22,24,25]. The application of QHJ to eigenvalues has been explored in great detail by Bhalla, Kapoor and collaborators [26][27][28][29][30][31][32][33]. QES systems have been also studied within QHJ approach [31].…”

Section: Introductionmentioning

confidence: 98%

Solutions of Two-Mode Bosonic and Transformed Hamiltonians

2007

View full text Add to dashboard Cite

We have constructed the quasi-exactly-solvable two-mode bosonic realization of SU(2). Two-mode boson Hamiltonian is defined through a differential equation which is solved by quantum Hamilton-Jacobi formalism. The squeezed states of two-mode boson systems are characterized through canonical transformation. The illustrated concept of squeezed boson systems has been applied two-mode bosonic Hamiltonian which is a squeezed one and is determined through a differential equation. This differential equation is solved and energy eigenvalues are found approximately.

show abstract

Section: Introductionmentioning

confidence: 98%

Solutions of Two-Mode Bosonic and Transformed Hamiltonians

2007

View full text Add to dashboard Cite

show abstract

“…They can only be poles with residue −ih. Suppose b = 0 then, moving singularities are in the form of [30][31][32][33][34][35][36][37] …”

Section: Quantum Hamilton-jacobi Formalismmentioning

confidence: 99%

“…gives the exact energy eigenvalues (n = 0, 1, 2, ...) [28][29][30][31][32][33]. Leacock [28,29] defines the wave function in order to connect QHJ equation to the Schödinger equation,…”

Section: Quantum Hamilton-jacobi Formalismmentioning

confidence: 99%

“…It was formulated by Leacock and Padgett in 1983 [28-29]. Within the Quantum Hamiltonian Jacobi approach (QHJ), which follows classical mechanics, not only the the energy spectrum of exactly solvable (ES) and quasi-exactly solvable (QES) models in quantum mechanics but eigenfunctions can also be determined [30][31][32][33][34][35][36]. The advantage of this method is that it is possible to determine the energy eigenvalues without having to solve for the eigenfunctions.…”

Section: Introductionmentioning

confidence: 99%

“…The advantage of this method is that it is possible to determine the energy eigenvalues without having to solve for the eigenfunctions. In this formalism, singularity structure of the quantum momentum function There is a boundary condition in the limit QMF which is used to determine physically acceptable solutions for the QMF [29][30][31][32][33][34][35][36][37]. In the applications, Ranjani and her collaborators applied the QHJ formalism, to Hamiltonians with Khare-Mandal potential and Scarf potential, characterized by discrete parity and time reversal (PT) symmetries [31].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Exponential type complex and non-Hermitian potentials within quantum Hamilton–Jacobi formalism

Yesiltas

Sever

2007

J Math Chem

View full text Add to dashboard Cite

show abstract

Wave Equations in Higher Dimensions

Dong

2011

224

153

View full text Add to dashboard Cite

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...

show abstract

Bound states and band structure—A unified treatment through the quantum Hamilton–Jacobi approach

Cited by 17 publications

References 18 publications

Solutions of Two-Mode Bosonic and Transformed Hamiltonians

Solutions of Two-Mode Bosonic and Transformed Hamiltonians

Exponential type complex and non-Hermitian potentials within quantum Hamilton–Jacobi formalism

Wave Equations in Higher Dimensions

Contact Info

Product

Resources

About