Abstract
We study semi-classical eigenvalues of a Schrödinger operator with delta-potential on 2D or 3D symmetric manifold. We describe Lagrangian manifolds, corresponding to such eigenvalues and compute the asymptotics of eigenvalues for different values of the parameter, defining the operator. We describe also the effect of the jump of the Maslov index while passing through the critical value of this parameter. These results were obtained in a number of joint papers with T. Filatova, T. Ratiu and A. Suleimanova.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Shafarevich, A.I. (2018). Lagrangian Manifolds and Maslov Indices Corresponding to the Spectral Series of the Schrödinger Operators with Delta-potentials. In: Kielanowski, P., Odzijewicz, A., Previato, E. (eds) Geometric Methods in Physics XXXV . Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-63594-1_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-63594-1_12
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-63593-4
Online ISBN: 978-3-319-63594-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)