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Analytic Feynman integral solutions of an integral equation related to the Schrödinger equation. (English) Zbl 0487.45008


MSC:

45K05 Integro-partial differential equations
28C20 Set functions and measures and integrals in infinite-dimensional spaces (Wiener measure, Gaussian measure, etc.)
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic geometry
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References:

[1] S. Albeverio and R. Höegh-Krohn,Mathematical theory of Feynman path integrals, Preprint series. Institute of Mathematics, University of Oslo, 1974. · Zbl 0337.28009
[2] Albeverio, S.; Höegh-Krohn, R., Feynman path integrals and the corresponding method of stationary phase, 3-57 (1978), Berlin: Springer-Verlag, Berlin · Zbl 0424.28014
[3] R. H. Burkhart.A rigorous development of Feynman’s original path integral, University of North Carolina at Wilmington, Dec. 1978, preprint.
[4] Cameron, R. H., The ilstow and Feynman integrals, J. Analyse Math., 10, 287-361 (1962) · Zbl 0133.07701 · doi:10.1007/BF02790311
[5] Cameron, R. H.; Martin, W. T., An unsymmetric Fubini theorem, Bull. Amer. Math. Soc., 47, 121-125 (1941) · Zbl 0025.15201 · doi:10.1090/S0002-9904-1941-07384-2
[6] R. H. Cameron and D. A. Storvick,Some Banach algebras of analytic Feynman integrable functionals. Proceedings of Seventh International Conference on Analytic Functions, Kozubnik, Poland, to appear. · Zbl 0439.28007
[7] Johnson, G. W.; Skoug, D. L., A Banach algebra of Feynman integrabe functionals with application to an integral equation formally equivalent to Schroedinger’s Equation, J. Functional Analysis, 12, 129-152 (1973) · Zbl 0255.46041 · doi:10.1016/0022-1236(73)90019-0
[8] Tarski, J., Feynman-type integrals defined in terms of general cylindrical approximations, 254-279 (1978), Berlin: Springer-Verlag, Berlin
[9] Truman, A., The polygonal path formulation of the Feynman path integral, 73-102 (1978), Berlin: Springer-Verlag, Berlin · Zbl 0412.28009
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