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Green’s Functions For Generalized Schroedinger Equations*

Published online by Cambridge University Press:  22 January 2016

John A. Beekman
John A. Beekman*
Affiliation:
Ball State UniversityMuncie, Indiana
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I. Introduction. The purpose of this paper is to discuss functions defined on the continuous sample paths of Gaussian Markov processes which serve as Green’s functions for pairs of generalized Schroedinger equations. The results extend the author’s earlier paper [2] to a forward time version, and consider different boundary conditions.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 35 , July 1969 , pp. 133 - 150
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1969

Footnotes

*

This research was partially supported by the National Science Foundation through grant NSF GP–7639.

References

[1] Beekman, John A., “Solutions to Generalized Schroedinger Equations via Feynman Integrals Connected with Gaussian Markov Stochastic Processes,” Thesis, U. of Minnesota, 1963.Google Scholar
[2] Beekman, John A., “Gaussian Processes and Generalized Schroedinger Equations,” J. Math and Mech. 14 (1965), 789–806.Google Scholar
[3] Beekman, John A., “Gaussian Markov Processes and a Boundary Value Problem,” Trans. Amer. Math. Soc. 126 (1967), 29–42.Google Scholar
[4] Beekman, John A., “Feynman-Cameron Integrals,” J. Math, and Physics, 46 (1967), 253–266.Google Scholar
[5] Cameron, R.H., “A Family of Integrals Serving to Connect the Wiener and Feynman Integrals,” J. of Math, and Physics, 39 (1960), 126–140.Google Scholar
[6] Cameron, R.H. and Donsker, M.D., “Inversion Formulae for Characteristic Functionals of Stochastic Processes,” Ann. of Math., 69 (1959), 15–36.Google Scholar
[7] Donsker, M.D. and Lions, J.L., “Fréchet-Volterra Variational Equations, Boundary Value Problems, and Function Space Integrals,” Acta Mathematica, 108 (1962), 142–228.Google Scholar
[8] Feynman, R.P. and Hibbs, A.R., Quantum Mechanics and Path Integrals, McGraw-Hill, New York, 1965.Google Scholar
[9] Fosdick, Lloyd D., “Approximation of a Class of Wiener Integrals,” Math, of Computation, 19 (1965), 225–233.Google Scholar
[10] Itô, Kiyosi, “Generalized Uniform Complex Measures in the Hilbertian Metric Space with their Application to the Feynman Integral,” Proc. Fifth Berkeley Symposium on Math. Statistics and Probability, Vol. II, Part 1 (1967), Univ. of Calif. Press, 145–161.Google Scholar
[11] Kac, Mark, Probability and Related Topics in Physical Sciences, Intersciénce Publishers, New York, 1959.Google Scholar
[12] Kac, Mark, “Random Walk in the Presence of Absorbing Barriers,” Ann. Math. Statist. 16, 62–67.Google Scholar
[13] Kac, Mark and Siegert, A.J.F., “On the Theory of Noise in Radio Receivers with Square Law Detectors,” J. of Applied Physics, 18 (1947), 383–397.Google Scholar
[14] Wilks, S.S., Mathematical Statistics, Wiley, New York, 1962.Google Scholar