Back to Search
Start Over
Spectral gaps of 1-D Robin Schrödinger operators with single-well potentials.
- Source :
-
Journal of Mathematical Physics . Sep2020, Vol. 61 Issue 9, p1-15. 15p. - Publication Year :
- 2020
-
Abstract
- We prove sharp lower bounds on the spectral gap of 1-dimensional Schrödinger operators with Robin boundary conditions for each value of the Robin parameter. In particular, our lower bounds apply to single-well potentials with a centered transition point. This result extends the work of Cheng et al. [Comput. Math. Appl. 60(9), 2556–2563 (2010)] and Horváth [Proc. Am. Math. Soc. 131(4), 1215–1224 (2002)] in the Neumann and Dirichlet endpoint cases to the interpolating regime. We also build on the recent work by Andrews, Clutterbuck, and Hauer (arXiv:2002.06900) in the case of convex and symmetric single-well potentials. In particular, we show that the spectral gap is an increasing function of the Robin parameter for symmetric potentials. [ABSTRACT FROM AUTHOR]
- Subjects :
- *SCHRODINGER operator
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00222488
- Volume :
- 61
- Issue :
- 9
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Physics
- Publication Type :
- Academic Journal
- Accession number :
- 146176574
- Full Text :
- https://doi.org/10.1063/5.0015671