Skip to main content
SpringerLink
Log in
Book cover

Principles of Advanced Mathematical Physics

  • Textbook
  • © 1978

Overview

Authors:
  1. Robert D. Richtmyer

    1. Department of Physics and Astrophysics, University of Colorado, Boulder, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Theoretical and Mathematical Physics (TMP)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (17 chapters)

  1. Front Matter

    Pages i-xv
    Download chapter PDF

  2. Hilbert Spaces

    • Robert D. Richtmyer
    Pages 1-18

  3. Distributions; General Properties

    • Robert D. Richtmyer
    Pages 19-42

  4. Local Properties of Distributions

    • Robert D. Richtmyer
    Pages 43-51

  5. Tempered Distributions and Fourier Transforms

    • Robert D. Richtmyer
    Pages 52-67

  6. L2 Spaces

    • Robert D. Richtmyer
    Pages 68-98

  7. Some Problems Connected with the Laplacian

    • Robert D. Richtmyer
    Pages 99-124

  8. Linear Operators in a Hilbert Space

    • Robert D. Richtmyer
    Pages 125-142

  9. Spectrum and Resolvent

    • Robert D. Richtmyer
    Pages 143-157

  10. Spectral Decomposition of Self-Adjoint and Unitary Operators

    • Robert D. Richtmyer
    Pages 158-189

  11. Ordinary Differential Operators

    • Robert D. Richtmyer
    Pages 190-221

  12. Some Partial Differential Operators of Quantum Mechanics

    • Robert D. Richtmyer
    Pages 222-240

  13. Compact, Hilbert-Schmidt, and Trace-Class Operators

    • Robert D. Richtmyer
    Pages 241-252

  14. Probability; Measures

    • Robert D. Richtmyer
    Pages 253-298

  15. Probability and Operators in Quantum Mechanics

    • Robert D. Richtmyer
    Pages 299-319

  16. Problems of Evolution; Banach Spaces

    • Robert D. Richtmyer
    Pages 320-334

  17. Well-Posed Initial-Value Problems; Semigroups

    • Robert D. Richtmyer
    Pages 335-363

  18. Nonlinear Problems: Fluid Dynamics

    • Robert D. Richtmyer
    Pages 364-408

  19. Back Matter

    Pages 409-424
    Download chapter PDF
Back to top

Keywords

About this book

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.

Authors and Affiliations

  • Department of Physics and Astrophysics, University of Colorado, Boulder, USA

    Robert D. Richtmyer

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation