A lower bound for the ground state energy of a Schrödinger operator on a loop

Author:
Helmut Linde

Journal:
Proc. Amer. Math. Soc. **134** (2006), 3629-3635

MSC (2000):
Primary 81Q10; Secondary 53A04

Published electronically:
May 31, 2006

MathSciNet review:
2240676

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Abstract | References | Similar Articles | Additional Information

Abstract: Consider a one-dimensional quantum mechanical particle described by the Schrödinger equation on a closed curve of length . 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 . We also prove that it is not lower than (the conjectured optimal lower bound) for a certain class of closed curves that have an additional geometrical property.

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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

DOI:
http://dx.doi.org/10.1090/S0002-9939-06-08483-8

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

Article copyright:
© Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.