The Wiener integral and the Schrödinger operator

Author:
Donald Babbitt

Journal:
Trans. Amer. Math. Soc. **116** (1965), 66-78

MSC:
Primary 35.77; Secondary 35.06

DOI:
https://doi.org/10.1090/S0002-9947-1965-0186926-9

Correction:
Trans. Amer. Math. Soc. **121** (1966), 549-552.

MathSciNet review:
0186926

Full-text PDF Free Access

References | Similar Articles | Additional Information

**[1]**Donald Babbitt,*The Wiener integral and perturbation theory of the Schrödinger operator*, Bull. Amer. Math. Soc.**70**(1964), 254–259. MR**161180**, https://doi.org/10.1090/S0002-9904-1964-11106-X**[2]**Donald G. Babbitt,*A summation procedure for certain Feynman integrals*, J. Mathematical Phys.**4**(1963), 36–41. MR**144665**, https://doi.org/10.1063/1.1703885**[3]**Nelson Dunford and Jacob T. Schwartz,*Linear operators. Part II: Spectral theory. Self adjoint operators in Hilbert space*, With the assistance of William G. Bade and Robert G. Bartle, Interscience Publishers John Wiley & Sons New York-London, 1963. MR**0188745****[4]**E. B. Dynkin,*Transformations of Markov processes connected with additive functionals*, Proc. 4th Berkeley Sympos. Math. Statist. and Prob., Vol. II, Univ. California Press, Berkeley, Calif., 1961, pp. 117–142. MR**0141159****[5]**E. B. Dynkin,*Additive functionals of a Wiener process determined by stochastic integrals*, Teor. Verojatnost. i Primenen.**5**(1960), 441–452 (Russian, with English summary). MR**0133163****[6]**-,*Markov processes and problems in analysis*, Amer. Math. Soc. Transl. (2)**31**(1963), 1-24.**[7]**Jacob Feldman,*On the Schrödinger and heat equations for nonnegative potentials*, Trans. Amer. Math. Soc.**108**(1963), 251–264. MR**160264**, https://doi.org/10.1090/S0002-9947-1963-0160264-0**[8]**R. K. Getoor,*Additive functionals of a Markov process*, Pacific J. Math.**7**(1957), 1577–1591. MR**94850****[9]**R. K. Getoor,*Markov operators and their associated semi-groups*, Pacific J. Math.**9**(1959), 449–472. MR**107297****[10]**Einar Hille and Ralph S. Phillips,*Functional analysis and semi-groups*, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, Providence, R. I., 1957. rev. ed. MR**0089373****[11]**Teruo Ikebe and Tosio Kato,*Uniqueness of the self-adjoint extension of singular elliptic differential operators*, Arch. Rational Mech. Anal.**9**(1962), 77–92. MR**142894**, https://doi.org/10.1007/BF00253334**[12]**Kiyosi Ito,*On stochastic differential equations*, Mem. Amer. Math. Soc.**No. 4**(1951), 51. MR**0040618****[13]**Seizô Itô,*Fundamental solutions of parabolic differential equations and boundary value problems*, Jap. J. Math.**27**(1957), 55–102. MR**0098240**, https://doi.org/10.4099/jjm1924.27.0_55**[14]**M. Kac,*On some connections between probability theory and differential and integral equations*, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, University of California Press, Berkeley and Los Angeles, 1951, pp. 189–215. MR**0045333****[15]**Tosio Kato,*Quadratic forms in Hilbert spaces and asymptotic perturbation series*, Department of Mathematics, University of California, Berkeley, Calif., 1955. MR**0073958****[16]**L. Landau and E. Lipshitz,*Quantum mechanics, non-relativistic theory*, Addison-Wesley, Reading, Mass., 1958.**[17]**Ju. Prokhorov,*Convergence of random processes and limit theorems in probability theory*, Appendix 2, Theor. Probability Appl.**1**(1956), 207-214.**[18]**Daniel Ray,*On spectra of second-order differential operators*, Trans. Amer. Math. Soc.**77**(1954), 299–321. MR**66539**, https://doi.org/10.1090/S0002-9947-1954-0066539-2**[19]**Kôsaku Yosida,*On the fundamental solution of the parabolic equation in a Riemannian space*, Osaka Math. J.**5**(1953), 65–74. MR**56177**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
35.77,
35.06

Retrieve articles in all journals with MSC: 35.77, 35.06

Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1965-0186926-9

Article copyright:
© Copyright 1965
American Mathematical Society