Advertisement

Self-Adjoint Operators. SchrÖdinger Operators

  • W. O. Amrein
Part of the Mathematical Physics Studies book series (MPST, volume 2)

Abstract

In Section 2.1 we define symmetric and self-adjoint operators and give criteria for a symmetric operator to be self-adjoint. In Section 2.2 we study simple spectral properties of self-adjoint operators. A particular class of self-adjoint operators, the socalled multiplication operators, are introduced in Section 2.3, and the results are applied to proving the essential self-adjointness of the Laplacian. In Section 2.4 we give a criterion for the invariance of self-adjointness under perturbations and apply it to Schrödinger operators with non-singular potentials. Finally, in Section 2.5, we give a characterization of the domain of Schrödinger operators with strongly singular potentials. The importance of self-adjointness will be discussed in Section 4.1.

Keywords

Multiplication Operator Symmetric Operator Linear Manifold Singular Potential Resolvent Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1981

Authors and Affiliations

  • W. O. Amrein
    • 1
  1. 1.Department of Theoretical PhysicsUniversity of GenevaSwitzerland

Personalised recommendations