Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

On Evgrafov–Fedoryuk’s theory and quadratic differentials

On Evgrafov–Fedoryuk’s theory and quadratic differentials The purpose of this note is to recall the theory of the (homogenized) spectral problem for Schrödinger equation with a polynomial potential and its relation with quadratic differentials. We derive from results of this theory that the accumulation rays of the eigenvalues of the latter problem are in $$1-1$$ 1 - 1 -correspondence with the short geodesics of the singular planar metrics induced by the corresponding quadratic differential. We prove that for a polynomial potential of degree $$d,$$ d , the number of such accumulation rays can be any positive integer between $$(d-1)$$ ( d - 1 ) and $$d \atopwithdelims ()2$$ d 2 . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

On Evgrafov–Fedoryuk’s theory and quadratic differentials

Analysis and Mathematical Physics , Volume 5 (2) – Feb 3, 2015

Loading next page...
 
/lp/springer-journals/on-evgrafov-fedoryuk-s-theory-and-quadratic-differentials-ltfYBIc8gc
Publisher
Springer Journals
Copyright
Copyright © 2015 by Springer Basel
Subject
Mathematics; Analysis; Mathematical Methods in Physics
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-014-0092-y
Publisher site
See Article on Publisher Site

Abstract

The purpose of this note is to recall the theory of the (homogenized) spectral problem for Schrödinger equation with a polynomial potential and its relation with quadratic differentials. We derive from results of this theory that the accumulation rays of the eigenvalues of the latter problem are in $$1-1$$ 1 - 1 -correspondence with the short geodesics of the singular planar metrics induced by the corresponding quadratic differential. We prove that for a polynomial potential of degree $$d,$$ d , the number of such accumulation rays can be any positive integer between $$(d-1)$$ ( d - 1 ) and $$d \atopwithdelims ()2$$ d 2 .

Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Feb 3, 2015

References