Skip to main content
SpringerLink
Log in

Absence of positive eigenvalues in a class of 2-body quantum systems with nonlocal interactions

Отсутствие подожительных собственных значений в классе двухчастичных квантовых систем с нелокальным взаимодействием

  • Published:
Il Nuovo Cimento A (1965-1970)

Summary

If we use the dilatation analytic techniques of Combes and results of Simon in the local situation, the absence of positive eigenvalues embedded in the continuum is proven for a suitable class of nonlocal 2-body Hamiltonians. Nuclear-physics nonlocal interactions are discussed.

Riassunto

Se si usano le tecniche analitiche di dilatazione di Combes e i risultati di Simon nella situazione locale, si dimostra l’assenza di autovalori positivi incastonati nel continuo per una classe adatta di hamiltoniani non locali di due corpi. Si discutono interazioni non locali di fisica nucleare.

Резюме

Используя аналитическую технику расширения Комбеса и результаты Симона в локальной ситуации, доказывается отсутствие положительных собственных значений, внедренных в континуум, для соответствующего класса нелинейных двухчастичных Гамильтонианов. Обсуждаются нелокальные взаимодействия в ядерной физике.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. T. Kato:Comm. Pure Appl. Math.,12, 403 (1959);S. Agmon:Journ. Anal. Math.,23, 1 (1970);B. Simon:Comm. Pure Appl. Math.,22, 531 (1969);J. Weidmann:Math. Zeit.,98, 268 (1967).

    Article  MATH  MathSciNet  Google Scholar 

  2. Y. Yamaguchi:Phys. Rev.,95, 1628, 1635 (1954).

    Article  MATH  ADS  Google Scholar 

  3. H. Feshbach:Ann. of Phys.,5, 357 (1958);19, 287 (1962);F. Perey andB. Buck:Nucl. Phys.,32, 353 (1962).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  4. M. Bertero, G. Talenti andG. Viano:Nuovo Cimento,46, 337 (1966);Comm. Math. Phys.,6, 128 (1967);Nucl. Phys.,113 A, 625 (1968);115 A, 395 (1968).

    Article  MATH  ADS  Google Scholar 

  5. K. Chadan:Nuovo Cimento,10, 892 (1958);47, 510 (1967).

    Article  MathSciNet  Google Scholar 

  6. M. Bolsterli:Phys. Rev.,182, 1095 (1969).

    Article  ADS  Google Scholar 

  7. P. Beregi:Nucl. Phys.,206 A, 217 (1973).

    Article  ADS  Google Scholar 

  8. T. Krause andB. Mulligan:Journ. Math. Phys.,15, 770 (1974).

    Article  MathSciNet  ADS  Google Scholar 

  9. J. Aguilar andJ. Combes:Comm. Math. Phys.,22, 269 (1971).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  10. B. Simon: preprint January 1973, 73/P, 515 Centre Physique Theoriques, CNRS, Marseille.

  11. A. J. O’Connor:Comm. Math. Phys.,32, 319 (1973).

    Article  MathSciNet  ADS  Google Scholar 

  12. J. Combes andL. Thomas:Comm. Math. Phys.,34, 251 (1973).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  13. E. C. Titchmarsh:The Theory of Functions (Oxford, 1932).

Download references

Author information

Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, New York University, New York, N. Y.

    F. Zirilli

Authors
  1. F. Zirilli
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Partially supported by the Italian National Research Council (CNR).

Traduzione a cura della Redazione.

Переведено редакцией.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zirilli, F. Absence of positive eigenvalues in a class of 2-body quantum systems with nonlocal interactions. Nuov Cim A 34, 385–390 (1976). https://doi.org/10.1007/BF02783617

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02783617

Search

Navigation