Advanced Studies in Pure Mathematics

On Spectral Theory for Schrödinger Operators with Magnetic Potentials

Bernard Helffer

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Abstract

In this survey, we want to analyze the effect of the presence of a magnetic potential on the spectrum of the Schrödinger operator with magnetic field. We consider three connected problems:

  • study of the bottom of the spectrum
  • study of the bottom of the essential spectrum
  • study of the decay of the eigenfunctions.
We think this survey is complementary to other presentations of the subject in [12], [20] and [49].

Article information

Source
Spectral and Scattering Theory and Applications, K. Yajima, ed. (Tokyo: Mathematical Society of Japan, 1994), 113-141

Dates
Received: 8 December 1992
First available in Project Euclid: 15 August 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1534359747

Digital Object Identifier
doi:10.2969/aspm/02310113

Zentralblatt MATH identifier
0816.35100

Citation

Helffer, Bernard. On Spectral Theory for Schrödinger Operators with Magnetic Potentials. Spectral and Scattering Theory and Applications, 113--141, Mathematical Society of Japan, Tokyo, Japan, 1994. doi:10.2969/aspm/02310113. https://projecteuclid.org/euclid.aspm/1534359747


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