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  • Conference proceedings
  • © 1991

Spectral Theory of Random Schrödinger Operators

A Genetic Introduction

Authors:

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1498)

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Table of contents (7 papers)

  1. Front Matter

    Pages I-VII
  2. Introduction

    • Reinhard Lang
    Pages 1-5
  3. Two simple examples

    • Reinhard Lang
    Pages 6-18
  4. The general heuristic picture

    • Reinhard Lang
    Pages 19-29
  5. Some known results and open problems

    • Reinhard Lang
    Pages 30-42
  6. Conclusion

    • Reinhard Lang
    Pages 113-118
  7. Back Matter

    Pages 119-125

About this book

The interplay between the spectral theory of Schr|dinger operators and probabilistic considerations forms the main theme of these notes, written for the non-specialist reader and intended to provide a brief and elementaryintroduction to this field. An attempt is made to show basic ideas in statu nascendi and to follow their evaluation from simple beginnings through to more advanced results. The term "genetic" in the title refers to this proceedure. The author concentrates on 2 topics which, in the history of the subject, have been of major conceptual importance - on the one hand the Laplacian is a random medium and the left end of its spectrum (leading to large deviation problems for Brownian motion and the link to thenotion of entropy) and on the other, Schr|dinger operators with general ergodic potentials in one-dimensional space. Ideas and concepts are explained in the simplest, possible setting and by means of a few characteristic problems with heuristic arguments preceding rigorous proofs.

Keywords

  • Brownian motion
  • Entropy
  • Large Deviations
  • Potential
  • Random Schroedinger Operators
  • Spectral Theory
  • Stochastic Analysis

Bibliographic Information

  • Book Title: Spectral Theory of Random Schrödinger Operators

  • Book Subtitle: A Genetic Introduction

  • Authors: Reinhard Lang

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0093929

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1991

  • Softcover ISBN: 978-3-540-54975-8Published: 11 December 1991

  • eBook ISBN: 978-3-540-46627-7Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 126

  • Topics: Probability Theory, Theoretical, Mathematical and Computational Physics

Buying options

eBook USD 29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 39.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions