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Principles of Advanced Mathematical Physics

  • Robert D. Richtmyer

Part of the Texts and Monographs in Physics book series (TMP)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Robert D. Richtmyer
    Pages 1-18
  3. Robert D. Richtmyer
    Pages 19-42
  4. Robert D. Richtmyer
    Pages 43-51
  5. Robert D. Richtmyer
    Pages 52-67
  6. Robert D. Richtmyer
    Pages 68-98
  7. Robert D. Richtmyer
    Pages 99-124
  8. Robert D. Richtmyer
    Pages 125-142
  9. Robert D. Richtmyer
    Pages 143-157
  10. Robert D. Richtmyer
    Pages 190-221
  11. Robert D. Richtmyer
    Pages 241-252
  12. Robert D. Richtmyer
    Pages 253-298
  13. Robert D. Richtmyer
    Pages 299-319
  14. Robert D. Richtmyer
    Pages 320-334
  15. Robert D. Richtmyer
    Pages 335-363
  16. Robert D. Richtmyer
    Pages 364-408
  17. Back Matter
    Pages 409-424

About this book

Introduction

A first consequence of this difference in texture concerns the attitude we must take toward some (or perhaps most) investigations in "applied mathe­ matics," at least when the mathematics is applied to physics. Namely, those investigations have to be regarded as pure mathematics and evaluated as such. For example, some of my mathematical colleagues have worked in recent years on the Hartree-Fock approximate method for determining the structures of many-electron atoms and ions. When the method was intro­ duced, nearly fifty years ago, physicists did the best they could to justify it, using variational principles, intuition, and other techniques within the texture of physical reasoning. By now the method has long since become part of the established structure of physics. The mathematical theorems that can be proved now (mostly for two- and three-electron systems, hence of limited interest for physics), have to be regarded as mathematics. If they are good mathematics (and I believe they are), that is justification enough. If they are not, there is no basis for saying that the work is being done to help the physicists. In that sense, applied mathematics plays no role in today's physics. In today's division of labor, the task of the mathematician is to create mathematics, in whatever area, without being much concerned about how the mathematics is used; that should be decided in the future and by physics.

Keywords

Fourier transform Functionals Hamiltonian Maxwell’s equations Monte Carlo method Potential applied mathematics conservation law mathematical physics mechanics momentum polarization quantum mechanics solution vector field

Authors and affiliations

  • Robert D. Richtmyer
    • 1
  1. 1.Department of Physics and AstrophysicsUniversity of ColoradoBoulderUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-46378-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 1978
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-46380-8
  • Online ISBN 978-3-642-46378-5
  • Series Print ISSN 1864-5879
  • Series Online ISSN 1864-5887
  • Buy this book on publisher's site
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