Download or read book Asymptotic Forms of Coulomb Wave Functions II written by Arthur Erdélyi and published by . This book was released on 1955 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Forms of Coulomb Wave Functions written by Arthur Erdélyi and published by . This book was released on 1955 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Forms of Whittaker s Confluent Hypergeometric Functions written by Arthur Erdélyi and published by American Mathematical Soc.. This book was released on 1957 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Coulomb Wave Functions written by Johan G. F. Belinfante and published by . This book was released on 1962 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Methods in Quantum Mechanics written by S.H. Patil and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum mechanics and the Schrodinger equation are the basis for the de scription of the properties of atoms, molecules, and nuclei. The development of reliable, meaningful solutions for the energy eigenfunctions of these many is a formidable problem. The usual approach for obtaining particle systems the eigenfunctions is based on their variational extremum property of the expectation values of the energy. However the complexity of these variational solutions does not allow a transparent, compact description of the physical structure. There are some properties of the wave functions in some specific, spatial domains, which depend on the general structure of the Schrodinger equation and the electromagnetic potential. These properties provide very useful guidelines in developing simple and accurate solutions for the wave functions of these systems, and provide significant insight into their physical structure. This point, though of considerable importance, has not received adequate attention. Here we present a description of the local properties of the wave functions of a collection of particles, in particular the asymptotic properties when one of the particles is far away from the others. The asymptotic behaviour of this wave function depends primarily on the separation energy of the outmost particle. The universal significance of the asymptotic behaviour of the wave functions should be appreciated at both research and pedagogic levels. This is the main aim of our presentation here.
Download or read book Table of Coulomb Wave Functions written by Carl Erik Fröberg and published by . This book was released on 1954 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Coulomb Wave Functions written by Alan Robert Curtis and published by . This book was released on 1964 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Tables of Nonrelativistic Coulomb Wave Functions written by Arnold Tubis and published by . This book was released on 1957 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Tables of Coulomb Wave Functions written by United States. National Bureau of Standards and published by . This book was released on 1952 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Expansions for Ordinary Differential Equations written by Wolfgang Wasow and published by Courier Dover Publications. This book was released on 2018-03-21 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This outstanding text concentrates on the mathematical ideas underlying various asymptotic methods for ordinary differential equations that lead to full, infinite expansions. "A book of great value." — Mathematical Reviews. 1976 revised edition.
Download or read book Nuclear Reactions II Theory Kernreaktionen II Theorie written by S. Flügge and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: 449 one finds that for y = Fo (e) C= :n; V3 [Po (2'Yj) 3 -kjF(i) + (2'Yj)! Fd (2'Yj) 3 -ijF (·m, } 1 (14.17) C2 = :n; [- (2'Yj)! Fd (2'Yj) 3 -ijF(i) + Fo (2'Yj) 3 -~;r(i)J, and if y is to be Go(e), C and Chave the same form with Go (2'Yj) replacing Po (2'Yj) 1 2 and G~(2'Yj) replacing Fd(2'Yj). The values of the functions at eo =2'Yj may be ob tained from (14.8). 1 J.K. TYSON has employed the modified Hankel functions of order one third 2 as solutions of (13.4) to obtain expressions for the Coulomb functions for L =0 which converge near e =2'Yj. His results appear as linear combinations of the real and imaginary parts of n ~(x) = (12)!e- ;/6 [A;{- x) - iB;( -x)J, (14.18) and its derivatives multiplying power series in x = (e - 2'Yj)j(2'Yj)1. For values 1 away from the turning point for L =0, TYSON has obtained forms for Po{e) and Go(e) which are similar to (13.1) to (13.3). The JWKB approximation is again the leading term, and some higher order corrections are given. Expressions similar to Eqs. (14.11) and (14.12) have been obtained by T.D. 3 NEWTON employing the integral representation of (4.4). His results give re presentations of FL(e), Gde) in the vicinity of e=2'Yj [whereas (14.11), (14.12) converge near e=eLJ when L.
Download or read book Theoretical Atomic Physics written by Harald Siegfried Friedrich and published by Springer Science & Business Media. This book was released on 2005-09-02 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: This established text contains an advanced presentation of quantum mechanics adapted to the requirements of modern atomic physics. The third edition extends the successful second edition with a detailed treatment of the wave motion of atoms, and it also contains an introduction to some aspects of atom optics that are relevant for current and future experiments involving ultra-cold atoms. Included: Various problems with complete solutions.
Download or read book Tables of Coulomb Wave Functions written by A. V. Luk'Yanov and published by Elsevier. This book was released on 2013-10-22 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tables of Coulomb Wave Functions (Whittaker Functions) focuses on tables compiled in the Mathematical Physics Department in conjunction with the Nuclear Reactions Laboratory of the Nuclear Physics Research Institute of Moscow State University. The book first states that Coulomb wave functions are used in the theory of nuclear reactions with charged particles, including protons, deuterons, and heavy ions. The text then offers information on the compilation and use of tables. The publication proceeds by highlighting the computations of various wave functions. These computations are presented in tabulated form. The manuscript also provides a list of volumes in the mathematical tables series. The book is a dependable source of data for scientists, engineers, and students working in the field of nuclear reactions.
Download or read book Tables of Coulomb Wave Functions written by United States. National Bureau of Standards and published by . This book was released on 1952 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotics of Linear Differential Equations written by M.H. Lantsman and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: The asymptotic theory deals with the problern of determining the behaviour of a function in a neighborhood of its singular point. The function is replaced by another known function ( named the asymptotic function) close (in a sense) to the function under consideration. Many problems of mathematics, physics, and other divisions of natural sci ence bring out the necessity of solving such problems. At the present time asymptotic theory has become an important and independent branch of mathematical analysis. The present consideration is mainly based on the theory of asymp totic spaces. Each asymptotic space is a collection of asymptotics united by an associated real function which determines their growth near the given point and (perhaps) some other analytic properties. The main contents of this book is the asymptotic theory of ordinary linear differential equations with variable coefficients. The equations with power order growth coefficients are considered in detail. As the application of the theory of differential asymptotic fields, we also consider the following asymptotic problems: the behaviour of explicit and implicit functions, improper integrals, integrals dependent on a large parameter, linear differential and difference equations, etc .. The obtained results have an independent meaning. The reader is assumed to be familiar with a comprehensive course of the mathematical analysis studied, for instance at mathematical departments of universities. Further necessary information is given in this book in summarized form with proofs of the main aspects.
Download or read book Gamow Shell Model written by Nicolas Michel and published by Springer Nature. This book was released on 2021-04-24 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the first graduate-level, self-contained introduction to recent developments that lead to the formulation of the configuration-interaction approach for open quantum systems, the Gamow shell model, which provides a unitary description of quantum many-body system in different regimes of binding, and enables the unification in the description of nuclear structure and reactions. The Gamow shell model extends and generalizes the phenomenologically successful nuclear shell model to the domain of weakly-bound near-threshold states and resonances, offering a systematic tool to understand and categorize data on nuclear spectra, moments, collective excitations, particle and electromagnetic decays, clustering, elastic and inelastic scattering cross sections, and radiative capture cross sections of interest to astrophysics. The approach is of interest beyond nuclear physics and based on general properties of quasi-stationary solutions of the Schrödinger equation – so-called Gamow states. For the benefit of graduate students and newcomers to the field, the quantum-mechanical fundamentals are introduced in some detail. The text also provides a historical overview of how the field has evolved from the early days of the nuclear shell model to recent experimental developments, in both nuclear physics and related fields, supporting the unified description. The text contains many worked examples and several numerical codes are introduced to allow the reader to test different aspects of the continuum shell model discussed in the book.
Download or read book Tables of Coulomb Wave Functions Volume Ii r written by MARTIN. BLUME and published by . This book was released on 1959 with total page 1 pages. Available in PDF, EPUB and Kindle. Book excerpt:
