Abstract
We investigate whether the eigenfunctions of the two-dimensional magnetic Schrödinger operator have a Gaussian decay of type exp(−Cx 2) at infinity (the magnetic field is rotationally symmetric). We establish this decay if the energy (E) of the eigenfunction is below the bottom of the essential spectrum (B), and if the angular Fourier components of the external potential decay exponentially (real analyticity in the angle variable). We also demonstrate that almost the same decay is necessary. The behavior ofC in the strong field limit and in the small (B−E) limit is also studied.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
K. Broderix, D. Hundertmark, H. Leschke, Continuity properties of Schrödinger semigroups with magnetic fields, In preparation.
H.L. Cycon, R.G. Froese, W. Kirsch, B. Simon, Schrödinger Operators with Application to Quantum Mechanics and Global Geometry, Springer-Verlag, 1987.
G.F. De Angelis, G. Jona-Lasinio, M. Sirugue, Probabilistic solution of Pauli type equations, J. Phys. A: Math. Gen. 16 (1983), 2433–2444.
M. Reed, B. Simon, Methods of Modern Mathematical Physics, Vol. IV., Academic Press, New York, 1979.
Author information
Authors and Affiliations
Additional information
Partial support from the Hungarian National Foundation for Scientific Research, grant no. 1902.
Rights and permissions
About this article
Cite this article
Erdős, L. Gaussian decay of the magnetic eigenfunctions. Geometric and Functional Analysis 6, 231–248 (1996). https://doi.org/10.1007/BF02247886
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02247886