Article PDF
References
Billingsley, P.: Convergence of probability measures. New York: Wiley 1968
Coddington, E.A., Levinson, N.: Theory of ordinary differential equations. New York: McGraw-Hill 1955
Frisch, H.L., Lloyd, S.P.: Electron levels in a one-dimensional random lattice. Phys. Rev. 120, 1175–1189 (1960)
Fukushima, M., Nagai, H., Nakao, S.: On an asymptotic property of spectra of a random difference operator. Proc. Japan Acad. 51, 100–102 (1975)
Halperin, B.I.: Green's functions for a particle in a one-dimensional random potential. Phys. Rev. 139 A, 104–117 (1965)
Ito, K.: Stochastic differentials. Appl. Math. and Optimization 1, 374–381 (1974)
Ito, K., McKean, H.P., Jr.: Diffusion processes and their sample paths. Berlin-Heidelberg-New York: Springer 1965
Kato, T.: Perturbation theory for linear operators. Berlin-Heidelberg-New York: Springer 1966
Kunita, H.: Diffusion processes and control systems. Lecture Note, Université de Paris VI, Lab. de calcul des probabilités, 1973–1974
Nakao, S.: On the spectral distribution of the Schrödinger operator with random potential. [To appear in Japan. J. Math.]
Pastur, L.S.: Spectra of random self-adjoint operator. Russian Math. Surveys 28, 1–67 (1973)
Ruelle, D.: Statistical mechanics. New York: Benjamin 1969
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Fukushima, M., Nakao, S. On spectra of the Schrödinger operator with a white Gaussian noise potential. Z. Wahrscheinlichkeitstheorie verw Gebiete 37, 267–274 (1977). https://doi.org/10.1007/BF00537493
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00537493