Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

The gap between the first two eigenvalues of a one-dimensional Schrödinger operator with symmetric potential


Author: S. Abramovich
Journal: Proc. Amer. Math. Soc. 111 (1991), 451-453
MSC: Primary 34L40; Secondary 34B05, 34L15, 47E05, 81Q10
MathSciNet review: 1036981
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove the inequality $ {\lambda _2}[{V_1}] - {\lambda _1}[{V_1}] \geq {\lambda _2}[{V_0}] - {\lambda _1}[{V_0}]$ for the difference of the first two eigenvalues of one-dimensional Schrödinger operators $ - \frac{{{d^2}}}{{d{x^2}}} + {V_i}(x),i = 0,1$, where $ {V_1}$ and $ {V_0}$ are symmetric potentials on $ (a,b)$ and on $ (a,(a + b)/2)$, and $ {V_0} - {V_1}$ is decreasing on $ (a,(3a + b)/4)$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 34L40, 34B05, 34L15, 47E05, 81Q10

Retrieve articles in all journals with MSC: 34L40, 34B05, 34L15, 47E05, 81Q10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1036981-X
PII: S 0002-9939(1991)1036981-X
Keywords: Schrödinger operators, eigenvalue gaps
Article copyright: © Copyright 1991 American Mathematical Society