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Alsholm, P.; Schmidt, G.

Spectral and scattering theory for Schrödinger operators. (English) Zbl 0226.35076

Arch. Ration. Mech. Anal. 40, 281-311 (1971).
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Cited in 1 Review
Cited in 33 Documents

MSC:

35P25 Scattering theory for PDEs
35J10 Schrödinger operator, Schrödinger equation
35P05 General topics in linear spectral theory for PDEs
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References:

[1] Alsholm, P., & G. Schmidt, Spectral and Scattering Theory for Schrödinger Operators, Various Publications Series, No. 7 Matematisk Institut Aarhus Universitet. · Zbl 0226.35075
[2] 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). · Zbl 0084.30402
[3] Dollard, J. D., Screening in the Schrödinger theory of scattering. J. Math. Phys. 9, 620–624 (1968). · doi:10.1063/1.1664618
[4] Dunford, N., & J. T. Schwartz, Linear Operators, I, II. New York: Interscience 1966–1967.
[5] Hellwig, G., Differentialoperatoren der Mathematischen Physik. Berlin-Göttingen-Heidelberg-New York: Springer 1964. · Zbl 0134.08602
[6] Ikebe, T., Eigenfunction expansions associated with the Schrödinger operators and their applications to scattering theory. Arch. Rational Mech. Anal. 5, 1–34 (1960). · Zbl 0145.36902 · doi:10.1007/BF00252896
[7] Ikebe, T., & T. Kato, Uniqueness of the self-adjoint extensions of singular elliptic differential operators. Arch. Rational Mech. Anal. 9, 77–92 (1962). · Zbl 0103.31801 · doi:10.1007/BF00253334
[8] Kato, T., Growth properties of solutions of the reduced wave equation with a variable coefficient. Comm. Pure Appl. Math. 12, 403–425 (1959). · Zbl 0091.09502 · doi:10.1002/cpa.3160120302
[9] Kato, T., Perturbation Theory for Linear Operators. Berlin-Heidelberg-New York: Springer 1966. · Zbl 0148.12601
[10] Kuroda, S. T., On the existence and the unitary property of the scattering operator. Nuovo Cimento 12, 431–454 (1959). · Zbl 0084.44801 · doi:10.1007/BF02745786
[11] 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).
[12] Kuroda, S. T., Perturbation of eigenfunction expansions. Proc. Nat. Acad. Sci. U.S.A. 57, 1213–1217 (1967). · Zbl 0154.16401 · doi:10.1073/pnas.57.5.1213
[13] Kuroda, S. T., An abstract stationary approach to perturbation of continuous spectra and scattering theory. J. Analyse Math. 20, 57–117 (1967). · Zbl 0153.16903 · doi:10.1007/BF02786670
[14] Povzner, A. Ja., The expansion of arbitrary functions in terms of eigenfunctions of the operator -{\(\Delta\)}u+cu. A.M.S. Translations, Series 2, 60, 1–49 (1967). · Zbl 0179.14504
[15] Rejto, P. A., On the essential spectrum of the hydrogen energy and related operators, Pacific J. Math. 19, 109–140 (1966). · Zbl 0144.17701 · doi:10.2140/pjm.1966.19.109
[16] Riesz, F., & B. Sz.-Nagy, Functional Analysis. F. Ungar. Publ. Co. 1955.
[17] Schmidt, G., On the representation of the potential scattering operator in quantum mechanics. J. of Diff. Equations 7, No. 2, 389–394 (1970). · Zbl 0188.41002 · doi:10.1016/0022-0396(70)90117-8
[18] Shenk, N. A., Eigenfunction expansions and scattering theory for the wave equation in an exterior region. Arch. Rational Mech. Anal. 21, 120–150 (1966). · Zbl 0135.15602 · doi:10.1007/BF00266571
[19] Titchmarsh, E. C., Eigenfunction Expansions Associated with Second-Order Differential Equations. II. Oxford: Clarendon Press 1958. · Zbl 0097.27601
[20] Thoe, D. W., Spectral theory for the wave equation with a potential term. Arch. Rational Mech. Anal. 22, 364–406 (1966). · Zbl 0143.33101 · doi:10.1007/BF00266560
[21] Thoe, D. W., Eigenfunction expansions associated with Sch · Zbl 0168.12501 · doi:10.1007/BF00281639
[22] Watson, G., A Treatise on the Theory of Bessel Functions, 2nd Edition. Cambridge: University Press 1952.
[23] Yosida, K., Functional Analysis. Berlin-Heidelberg-New York: Springer 1965. · Zbl 0126.11504
[24] Zemach, C., & F. Odeh, Uniqueness of radiative solutions to the Schrödinger wave equation. Arch. Rational Mech. Anal. 5, 226–237 (1960). · Zbl 0136.09201 · doi:10.1007/BF00252905
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