References
Alsholm, P., & G. Schmidt, Spectral and Scattering Theory for Schrödinger Operators, Various Publications Series, No. 7 Matematisk Institut Aarhus Universitet.
Aronszajn, N., A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order. Jour. Math. Pures et Appl. 36, 235–249 (1957).
Dollard, J. D., Screening in the Schrödinger theory of scattering. J. Math. Phys. 9, 620–624 (1968).
Dunford, N., & J. T. Schwartz, Linear Operators, I, II. New York: Interscience 1966–1967.
Hellwig, G., Differentialoperatoren der Mathematischen Physik. Berlin-Göttingen-Heidelberg-New York: Springer 1964.
Ikebe, T., Eigenfunction expansions associated with the Schrödinger operators and their applications to scattering theory. Arch. Rational Mech. Anal. 5, 1–34 (1960).
Ikebe, T., & T. Kato, Uniqueness of the self-adjoint extensions of singular elliptic differential operators. Arch. Rational Mech. Anal. 9, 77–92 (1962).
Kato, T., Growth properties of solutions of the reduced wave equation with a variable coefficient. Comm. Pure Appl. Math. 12, 403–425 (1959).
Kato, T., Perturbation Theory for Linear Operators. Berlin-Heidelberg-New York: Springer 1966.
Kuroda, S. T., On the existence and the unitary property of the scattering operator. Nuovo Cimento 12, 431–454 (1959).
Kuroda, S. T., Construction of eigenfunction expansions by the perturbation method and its application to n-dimensional Schrödinger operators. MRC Technical Summary Report No. 744 (1967).
Kuroda, S. T., Perturbation of eigenfunction expansions. Proc. Nat. Acad. Sci. U.S.A. 57, 1213–1217 (1967).
Kuroda, S. T., An abstract stationary approach to perturbation of continuous spectra and scattering theory. J. Analyse Math. 20, 57–117 (1967).
Povzner, A. Ja., The expansion of arbitrary functions in terms of eigenfunctions of the operator -Δu+cu. A.M.S. Translations, Series 2, 60, 1–49 (1967).
Rejto, P. A., On the essential spectrum of the hydrogen energy and related operators, Pacific J. Math. 19, 109–140 (1966).
Riesz, F., & B. Sz.-Nagy, Functional Analysis. F. Ungar. Publ. Co. 1955.
Schmidt, G., On the representation of the potential scattering operator in quantum mechanics. J. of Diff. Equations 7, No. 2, 389–394 (1970).
Shenk, N. A., Eigenfunction expansions and scattering theory for the wave equation in an exterior region. Arch. Rational Mech. Anal. 21, 120–150 (1966).
Titchmarsh, E. C., Eigenfunction Expansions Associated with Second-Order Differential Equations. II. Oxford: Clarendon Press 1958.
Thoe, D. W., Spectral theory for the wave equation with a potential term. Arch. Rational Mech. Anal. 22, 364–406 (1966).
Thoe, D. W., Eigenfunction expansions associated with Schrödinger operators in R n, n≧4. Arch. Rational Mech. Anal. 26, 335–356 (1967).
Watson, G., A Treatise on the Theory of Bessel Functions, 2nd Edition. Cambridge: University Press 1952.
Yosida, K., Functional Analysis. Berlin-Heidelberg-New York: Springer 1965.
Zemach, C., & F. Odeh, Uniqueness of radiative solutions to the Schrödinger wave equation. Arch. Rational Mech. Anal. 5, 226–237 (1960).
Author information
Authors and Affiliations
Additional information
Communicated by M. M. Schiffer
Rights and permissions
About this article
Cite this article
Alsholm, P., Schmidt, G. Spectral and scattering theory for Schrödinger operators. Arch. Rational Mech. Anal. 40, 281–311 (1971). https://doi.org/10.1007/BF00252679
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00252679