Pacific Journal of Mathematics

Notes on the Feynman integral. III. The Schroedinger equation.

G. W. Johnson and D. L. Skoug

Article information

Source
Pacific J. Math. Volume 105, Number 2 (1983), 321-358.

Dates
First available: 8 December 2004

Permanent link to this document
http://projecteuclid.org/euclid.pjm/1102723333

Zentralblatt MATH identifier
0505.28010

Zentralblatt MATH identifier
0459.28013

Mathematical Reviews number (MathSciNet)
MR691608

Subjects
Primary: 81C35
Secondary: 28B05: Vector-valued set functions, measures and integrals [See also 46G10] 46G99: None of the above, but in this section 58D30: Applications (in quantum mechanics (Feynman path integrals), relativity, fluid dynamics, etc.)

Citation

Johnson, G. W.; Skoug, D. L. Notes on the Feynman integral. III. The Schroedinger equation. Pacific Journal of Mathematics 105 (1983), no. 2, 321--358. http://projecteuclid.org/euclid.pjm/1102723333.


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References

  • [1] S. Albeverio and R. Heegh-Krohn, Mathematical Theory of Feynman Path Integrals, Springer Lecture Notes in Mathematics, Vol. 523,Berlin, 1976.
  • [2] S. Albeverio and R. Heegh-Krohn, Feynman path integrals and the corresponding method of stationary phase, in Feynman Path Integrals, Marseille, 1978, Springer Lecture Notes in Physics, Vol. 106, Berlin, 1979,3-57.
  • [3] R. H. Cameron and W. T. Martin, An unsymmetric Fubini theorem, Bull. Amer. Math. Soc, 47 (1941), 121-125.
  • [4] R. H. Cameron and D. A. Storvick, Some Banach algebras of analytic Feynman integrable functionals, in Analytic Functions, Kozubnik, 1979, Springer Lecture Notes in Mathematics, Vol. 798, Berlin, 1980.
  • [5] R. H. Cameron and D. A. Storvick, Analytic Feynman integral solutions of an integral equation related to the Schroedinger equation, J. D'Analyse Math., 38 (1980), 34-66.
  • [6] S. D. Chatterji, Disintegration of Measures and Lifting, in Vector and Operator Valued Measures and Applications, Academic Press, New York, 1973, 69-83.
  • [7] B. R. Gelbaum and J. M. H. Olmsted, Counterexamples in Analysis, Holden-Day, San Francisco, 1964.
  • [8] P. R. Halmos, Measure Theory, Van Nostrand, Princeton, 1950.
  • [9] G. W. Johnson, The equivalence of two approaches to the Feynman integral, to appear in J. Math. Physics.
  • [10] G. W. Johnson, An unsymmetric Fubini theorem, submitted for publication.
  • [11] G. W. Johnson and D. L. Skoug, Scale-invariant measurability in Wiener space, Pacific J. Math., 83 (1979), 157-176.
  • [12] G. W. Johnson and D. L. Skoug, Notes on the Feynman integral, I, Pacific J. Math., 93 (1981), 313-324.
  • [13] G. W. Johnson and D. L. Skoug, Notes on the Feynman integral, II, J. Functional Analysis, 41 (1981), 277-289.
  • [14] D. Maharam, Strict disintegration of measures, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 32 (1975), 73-79.
  • [15] P. A. Meyer, Probability and Potentials, Blaisdell, Waltham, Massachusetts, 1966, 173-174.
  • [16] R. E. A. C. Paley, N. Wiener, and A. Zygmund, Notes on random functions, Math. Zeit, 37(1933), 647-688.
  • [17] A. Truman, The Polygonal Path formulation of the Feynman path integral, in Feynman Path Integrals, Marseille, 1978, Springer Lecture Notes in Physics, Vol. 106, Berlin, 1979, 73-102.

See also

  • I : G. W. Johnson, D. L. Skoug. Notes on the Feynman integral. I. Pacific Journal of Mathematics volume 93, issue 2, (1981), pp. 313-324.
  • : G. W. Johnson, D. L. Skoug. Notes on the Feynman integral. {II}. II [MR 85k:81070b] J. Funct. Anal. 41 1981 3 277--289.