×

On asymptotic behaviour of the spectra of a one-dimensional Hamiltonian with a certain random coefficient. (English) Zbl 0362.34043


MSC:

34F05 Ordinary differential equations and systems with randomness
34L99 Ordinary differential operators
70H05 Hamilton’s equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Lax, M. and Phillips, J. C., One-dimensional impurity bands, Phys. Rev., 110 (1958), 41-49. · Zbl 0080.44906 · doi:10.1103/PhysRev.110.41
[2] Lifsic, I. M., Energy spectrum structure and quantum states of disordered condensed systems, Soviet Phys. Uspekhi, 7 (1965), 549-573.
[3] Frisch, H. L. and Lloyd, S. P., Electron levels in one-dimensional lattice, Phys. Rev., 120 (1960), 1175-1189. · Zbl 0093.23202 · doi:10.1103/PhysRev.120.1175
[4] Benderskii, M. M. and Pastur, L. A., On the spectrum of the one-dimensional Schrodinger equation with a random potential, Mat. Sb., 82 (1970), 273-284.
[5] , Calculation of the average number of states in a model problem, Soviet Phys. JETP, 30 (1970), 158-162.
[6] Eggarter, T. P., Some exact results on electron energy levels in certain one-dimen- sional random potentials, Phys. Rev., B, 5 (1972), 3863-3865.
[7] Pastur, L. A., Spectra of random self-adjoint operator, Russian Math. Surveys, 28 (1973), 1-69. · Zbl 0277.60049 · doi:10.1070/rm1973v028n01ABEH001396
[8] Fukushima, M. and Nakao, S., On spectra of the Schrodinger operator with a white Gaussian noise potential, to appear in Z. Wahrscheinlichkeitstheorie verw. Gebiete. · Zbl 0361.60044 · doi:10.1007/BF00537493
[9] Nakao, S., On the spectral distribution of the Schrodinger operator with random potential, to appear. · Zbl 0375.60067
[10] Kac, I. S. and Krein, M. G., On spectral functions of a string, Amer. Math. Soc. Transl. (2), 103 (1974), 19-102. · Zbl 0291.34017
[11] Levin, B. Ja., Distribution of zeros of entire functions, Transl. Math. Monographs 5, Amer. Math. Soc., Providence, R. L, 1964. · Zbl 0152.06703
[12] Bellman, R., Stability theory of differential equations, Dover Publications, Inc. New York, 1953. · Zbl 0053.24705
[13] Titchmarsh, E. C., Eigenfunction expansions, part 2, Oxford, 1962. · Zbl 0099.05201
[14] Fukushima, M., On the spectral distribution of a disordered system and the range of a random walk, Osaka J. Math., 11 (1974), 73-85. · Zbl 0366.60099
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.