Arkiv för Matematik

, 14:277 | Cite as

Eigenfunction expansions for the Schrödinger operator

  • Martin Schechter


We obtain an eigenfunction expansion for the operator −°+V under assump-tions (1.2)–(1.5) given below.


Weak Solution Elliptic Operator Accumulation Point Form Extension Wave Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Ikebe, T., Eigenfunction expansions associated with the Schrödinger operators and their applications to scattering theory.Arch. Rational Mech. Anal.,5 (1960), 1–34.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Povzner, A. Ja., The expansion of arbitrary functions in terms of eigenfunctions of the operator−Δu+cu, Math. Sb.,32 (1953), 109–156.MathSciNetGoogle Scholar
  3. 3.
    Shenk, N., Thoe, D., Eigenfunction expansions and scattering theory for perturbations of −Δ,J. Math. Anal. Appl.,36, (1971), 313–351.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Goldstein, C., Perturbations of nonselfadjoint operators, I, II.,Arch. Rational Mech. Anal.,37 (1970), 268–296,42 (1971), 380–402.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Alsholm, P., Schmidt, G., Spectral and scattering theory for Schrödinger operators,ibid.40, (1971), 281–311.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Schulenberger, J. R., Wilcox, C. H., Eigenfunction expansions and scattering theory for wave propagation problems of classical physics,ibid.46 (1972), 280–320.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Guillot, J. C., Schmidt, G., Spectral and scattering theory for Dirac operators.ibid.,55, (1974), 193–206.MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Guillot, J. C., Perturbation of the Laplacian by Coulomb like potentials,to appear.Google Scholar
  9. 9.
    Kuroda, S. T., Kato, T., Theory of simple scattering and eigenfunction expansions,Functional Analysis and Related Fields, Edited by F. E. Browder, Springer, 1970, 99–131.Google Scholar
  10. 10.
    Agmon, S., Spectral properties of Schrödinger operators and scattering theory.Ann. Scuola Norm. Sup. Pisa, Serie IV, Vol.2 (1975), 151–218.MATHMathSciNetGoogle Scholar
  11. 11.
    Howland, J. S., A perturbation theoretic approach to eigenfunction expansion,J. Functional Analysis.,2 (1968), 1–23.MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Mochizuki, K., Eigenfunction expansions associated with the Schrödinger operator,Proc. Japan Acad.,43, (1967), 638–643.MATHMathSciNetGoogle Scholar
  13. 13.
    Faddeev, L. D.,Mathematical Aspects of the Three-Body Problem in the Quantum Scattering Theory, Israel Program for Scientific Translations, Jerusalem, 1965.MATHGoogle Scholar
  14. 14.
    Thompson, M., Eigenfunction expansions and scattering theory for perturbed elliptic partial differential equations,Comm. Pure Appl. Math.,15 (1972), 499–532.CrossRefGoogle Scholar
  15. 15.
    Berezarskii, Ju. M.,Expansions in Eigenfunctions of Selfadjoint Operators, American Math. Soc., Providence, 1968.Google Scholar
  16. 16.
    Greiner, P. C., Eigenfunction expansions and scattering theory for perturbed elliptic partial differential operators,Bull. Amer. Math. Soc. 70 (1964), 517–521.MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Kato, T.,Perturbation Theory for Linear Operators, Springer, N. Y., 1966.MATHGoogle Scholar
  18. 18.
    Schechter, M., Scattering tehory for second order elliptic operators,Ann. Mat. Pura Appl.,105 (1975), 313–331.MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Schechter, M., Scattering theory for second order elliptic operators of arbitrary order,Comment. Math. Helv.,49 (1974), 84–113.MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Schechter, M., Discreteness of the singular spectrum for Schrödinger operators,Math. Proc. Cambridge Philos. Soc. 80 (1976), 121–133.MATHMathSciNetCrossRefGoogle Scholar
  21. 21.
    Schechter, M., Hamiltonians for singular potentials,Indiana Univ. Math. J.,22 (1972), 483–503.MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Simon, B.,Quantum Mechanics for Hamiltonians defined as Quadratic Forms, Princeton Univ. Press, 1971.Google Scholar
  23. 23.
    Lax, P. D., Phillips, R. S.,Scattering Theory, Academic Press, N. Y., 1967.MATHGoogle Scholar

Copyright information

© Institut Mittag-Leffler 1976

Authors and Affiliations

  • Martin Schechter
    • 1
  1. 1.Belfer Graduate School of ScienceYeshiva UniversityNew YorkUSA

Personalised recommendations