A lower bound for the ground state energy of a Schrödinger operator on a loop
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- by Helmut Linde PDF
- Proc. Amer. Math. Soc. 134 (2006), 3629-3635 Request permission
Abstract:
Consider a one-dimensional quantum mechanical particle described by the Schrödinger equation on a closed curve of length $2\pi$. Assume that the potential is given by the square of the curve’s curvature. We show that in this case the energy of the particle cannot be lower than $0.6085$. We also prove that it is not lower than $1$ (the conjectured optimal lower bound) for a certain class of closed curves that have an additional geometrical property.References
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Additional Information
- Helmut Linde
- Affiliation: Department of Physics, Pontificia Universidad Católica de Chile, Casilla 306, Correo 22 Santiago, Chile
- Email: Helmut.Linde@gmx.de
- Received by editor(s): June 21, 2005
- Published electronically: May 31, 2006
- Additional Notes: This work was supported by DIPUC (Pontificia Universidad Católica de Chile).
- Communicated by: Mikhail Shubin
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 3629-3635
- MSC (2000): Primary 81Q10; Secondary 53A04
- DOI: https://doi.org/10.1090/S0002-9939-06-08483-8
- MathSciNet review: 2240676