Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. Avron, I. Herbst and B. Simon, Schrödinger operators with magnetic fields, I., General Interactions, Duke Math. J. 45 (1978), 847–883.
H. L. Cycon, R. G. Froese, W. Kirsch and B. Simon, Schrödinger Operators with Application to Quantum Mechanics and Global Geometry, Texts and Monographs in Physics, Springer-Verlag, New York/Berlin, 1987.
Y. Colin de Verdiere, L'asymptotique de Weyl pour les bouteilles magnétiques, Comm. Math. Phys. 105 (1986), 327–335.
B. A. Dubrovin and S. P. Novikov, Ground states in a periodic field, Magnetic Bloch functions and vector bundles, Soviet Math. Dokl. 22 (1980), 240–244.
A. Dufresnoy, Un exemple de champ magnétique dans R v, Duke Math. J. 50 (1983), 729–734.
H. Hess, R. Schrader and D. A. Uhlenbrock, Domination of semigroups and generalization of Kato's inequality, Duke Math. J. 44 (1977), 893–904.
B. Helffer, Effet d'Aharonov Bohm sur un état borné de l'équation de Schrödinger, Comm. Math. Phys. 119 (1988), 315–329.
B. Helffer and J. Sjöstrand, Equation de Schrödinger avec champ magnétique fort et équation de Harper, preprint.
W. Hunziker, Schrödinger operators with electric or magnetic fields, in Mathematical Problems in Theoretical Physics, Lecture Notes in Physics, Vol. 116, ed. by K. Osterwalder, Springer-Verlag, New York/Berlin, 1979, pp. 25–44.
T. Ikebe and T. Kato, Uniqueness of the self-adjoint extension of singular elliptic differential operators, Arch. Rational Mech. Anal. 9 (1962), 77–92.
A. Iwatsuka, The essential spectrum of two-dimensional Schrödinger operators with perturbed constant magnetic fields, J. Math. Kyoto Univ. 23 (1983), 475–480.
A. Iwatsuka, Examples of absolutely continuous Schrödinger operators in magnetic fields, Publ. RIMS, Kyoto Univ. 21 (1985), 385–401.
A. Iwatsuka, Magnetic Schrödinger operators with compact resolvent, J. Math. Kyoto Univ. 26 (1986), 357–374.
A. Iwatsuka, Essential self-adjointness of the Schrödinger operators with magnetic fields diverging at infinity, in preparation.
A. Iwatsuka, Landau level broadening by periodic perturbation in uniform magnetic fields, in preparation.
T. Kato, Remarks on Schrödinger operators with vector potentials, Integral Equations and Operator Theory 1 (1978), 103–113.
H. Leinfelder, Gauge invariance of Schrödinger operators and related spectral properties, J. Op. Theory 9 (1983), 163–179.
R. Lavine and M. O'Carroll, Ground state properties and lower bounds for energy levels of a particle in a uniform magnetic field and external potential, J. Math. Phys. 18 (1977), 1908–1912.
H. Leinfelder and C. G. Simader, Schrödinger operators with singular magnetic potentials, Math. Z. 176 (1981), 1–19.
F. Odeh and J. B. Keller, Partial differential equation with periodic coefficients and Bloch waves in crystals, J. Math. Phys. 5 (1964), 1499–1504.
M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. II, Academic Press, New York, 1975.
M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. IV, Academic Press, New York, 1978.
B. Simon, Maximal and minimal Schrödinger forms, J. Op. Theory 1 (1979), 37–47.
B. Simon, Kato's inequality and the comparison of semigroups, J. Funct. Anal. 32 (1979), 97–101.
H. Tamura, Asymptotic distribution of eigenvalues for Schrödinger operators with magnetic fields, Nagoya Math. J. 105 (1987), 49–69.
L. E. Thomas, Time dependent approach to scattering from impurities in a crystal, Comm. Math. Phys. 33 (1973), 335–343.
J. Zak, Magnetic translation groups I. II., Phys. Rev. 134-A (1966), 1602–1611.
J. Zak, Group theoretical consideration of Landau level broadening in crystals, Phys. Rev. 136-A (1964), 776–780.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1990 Springer-Verlag
About this paper
Cite this paper
Iwatsuka, A. (1990). On Schrödinger operators with magnetic fields. In: Fujita, H., Ikebe, T., Kuroda, S.T. (eds) Functional-Analytic Methods for Partial Differential Equations. Lecture Notes in Mathematics, vol 1450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084904
Download citation
DOI: https://doi.org/10.1007/BFb0084904
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-53393-1
Online ISBN: 978-3-540-46818-9
eBook Packages: Springer Book Archive