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Asymptotic Methods in Quantum Mechanics

Application to Atoms, Molecules and Nuclei

  • Book
  • © 2000

Overview

Authors:
  1. S. H. Patil

    1. Department of Physics, Indian Institute of Technology, Bombay, India

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    You can also search for this author in PubMed   Google Scholar

  2. K. T. Tang

    1. Department of Physics, Pacific Lutheran University, Tacoma, USA

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    You can also search for this author in PubMed   Google Scholar

  • This book is unique in its detailed description of this important approach to problems of quantum mechanics
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Series in Chemical Physics (CHEMICAL, volume 64)

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-XI
    Download chapter PDF

  2. Introduction

    • S. H. Patil, K. T. Tang
    Pages 1-3

  3. General Properties of Wave Functions

    • S. H. Patil, K. T. Tang
    Pages 5-20

  4. Two- and Three-Electron Atoms and Ions

    • S. H. Patil, K. T. Tang
    Pages 21-39

  5. Polarizabilities and Dispersion Coefficients

    • S. H. Patil, K. T. Tang
    Pages 41-68

  6. Asymptotically Correct Thomas-Fermi Model Density

    • S. H. Patil, K. T. Tang
    Pages 69-83

  7. Molecules and Molecular Ions with One and Two Electrons

    • S. H. Patil, K. T. Tang
    Pages 85-103

  8. Interaction of an Electron with Ions, Atoms, and Molecules

    • S. H. Patil, K. T. Tang
    Pages 105-125

  9. Exchange Energy of Diatomic Systems

    • S. H. Patil, K. T. Tang
    Pages 127-146

  10. Inter-atomic and Inter-ionic Potentials

    • S. H. Patil, K. T. Tang
    Pages 147-160

  11. Proton and Neutron Densities in Nuclei

    • S. H. Patil, K. T. Tang
    Pages 161-167

  12. Back Matter

    Pages 169-174
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Keywords

About this book

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.

Reviews

“This is a monograph … . It is intended for researchers and graduate students in chemical physics and related areas.” (Tuncay Aktosun, zbMATH 0947.81002, 2022)

Authors and Affiliations

  • Department of Physics, Indian Institute of Technology, Bombay, India

    S. H. Patil

  • Department of Physics, Pacific Lutheran University, Tacoma, USA

    K. T. Tang

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