Skip to main content

Schrödinger Operators

  • Chapter
  • First Online:
Spectral Theory

Part of the book series: Graduate Texts in Mathematics ((GTM,volume 284))

  • 5319 Accesses

Abstract

The development of spectral theory in the 20th century was motivated in large part by quantum mechanics. In this chapter we develop basic applications of spectral theory to the theory of Schrödinger operators.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 29.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 39.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 39.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

References

  1. Davies, E.B.: Spectral Theory and Differential Operators. Cambridge Studies in Advanced Mathematics, vol. 42. Cambridge University Press, Cambridge (1995)

    Google Scholar 

  2. Edmunds, D.E., Evans, W.D.: Spectral Theory and Differential Operators. Oxford Mathematical Monographs, Oxford University Press, Oxford (2018)

    Book  Google Scholar 

  3. Gustafson, S.J., Sigal, I.M.: Mathematical Concepts of Quantum Mechanics. Universitext, 2nd edn. Springer, Heidelberg (2011)

    Book  Google Scholar 

  4. Hall, B.C.: Quantum Theory for Mathematicians. Graduate Texts in Mathematics, vol. 267. Springer, New York (2013)

    Book  Google Scholar 

  5. Hislop, P.D., Sigal, I.M.: Introduction to Spectral Theory. Applied Mathematical Sciences, vol. 113. Springer, Berlin (1996). With applications to Schrödinger operators

    Chapter  Google Scholar 

  6. Kato, T.: Perturbation Theory for Linear Operators. Springer, Berlin (1995). Reprint of the 1980 edition

    Book  Google Scholar 

  7. Kato, T.: Fundamental properties of Hamiltonian operators of Schrödinger type. Trans. Am. Math. Soc. 70, 195–211 (1951)

    MATH  Google Scholar 

  8. Magnus, W., Winkler, S.: Hill’s Equation. Dover, New York (1979). Corrected reprint of the 1966 edition

    Google Scholar 

  9. Olver, F.W.J., Olde Daalhuis, A.B., Lozier, D.W., Schneider, B.I., Boisvert, R.F., Clark, C.W., Miller, B.R., Saunders, B.V.: NIST Digital Library of Mathematical Functions (2016). http://dlmf.nist.gov/. Release 1.0.19

  10. Reed, M., Simon, B.: Methods of Modern Mathematical Physics. II. Fourier Analysis, Self-adjointness. Academic, London (1975)

    Google Scholar 

  11. Reed, M., Simon, B.: Methods of Modern Mathematical Physics. IV. Analysis of Operators. Academic, London (1978)

    Google Scholar 

  12. Reed, M., Simon, B.: Methods of Modern Mathematical Physics. III. Scattering Theory. Academic, London (1979)

    Google Scholar 

  13. Rellich, F.: Störungstheorie der Spektralzerlegung. Math. Ann. 116, 555–570 (1939)

    Article  Google Scholar 

  14. Simon, B.: Semiclassical analysis of low lying eigenvalues. I. Nondegenerate minima: asymptotic expansions. Ann. Inst. H. Poincaré Sect. A (N.S.) 38, 295–308 (1983)

    Google Scholar 

  15. Teschl, G.: Ordinary Differential Equations and Dynamical Systems. Graduate Studies in Mathematics, vol. 140. American Mathematical Society, Providence (2012)

    Google Scholar 

  16. Yafaev, D.R.: Mathematical Scattering Theory. Analytic Theory. Mathematical Surveys and Monographs, vol. 158. American Mathematical Society, Providence (2010)

    Google Scholar 

  17. Zworski, M.: Semiclassical Analysis. Graduate Studies in Mathematics, vol. 138. American Mathematical Society, Providence (2012)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Borthwick, D. (2020). Schrödinger Operators. In: Spectral Theory. Graduate Texts in Mathematics, vol 284. Springer, Cham. https://doi.org/10.1007/978-3-030-38002-1_7

Download citation

Publish with us

Policies and ethics