Advanced Studies in Pure Mathematics

Eigenvalue Properties of Schrödinger Operators

W. D. Evans, Roger T. Lewis, and Yoshimi Saitō

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Abstract

In Evans–Lewis [5] and Evans–Lewis–Saitō [6], [7], [8], [9] we have been discussing conditions for the finiteness and for the infiniteness of bound states of Schrödinger-type operators using geometric methods. Here the ideas and results obtained so far are summarized and presented in an expository manner. These bound states correspond to eigenvalues below the essential spectrum of the operator. After basic results are presented, Schrödinger operators of atomic type will be discussed to show how these basic results can be applied to various types of $N$-body Schrödinger operators.

Article information

Source
Spectral and Scattering Theory and Applications, K. Yajima, ed. (Tokyo: Mathematical Society of Japan, 1994), 27-55

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

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1534359742

Digital Object Identifier
doi:10.2969/aspm/02310027

Zentralblatt MATH identifier
0807.35117

Citation

Evans, W. D.; Lewis, Roger T.; Saitō, Yoshimi. Eigenvalue Properties of Schrödinger Operators. Spectral and Scattering Theory and Applications, 27--55, Mathematical Society of Japan, Tokyo, Japan, 1994. doi:10.2969/aspm/02310027. https://projecteuclid.org/euclid.aspm/1534359742


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