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

2005/08/11 by Helmut Linde, Linde, Helmut · 1 citation
Mathematics · Physics and Astronomy · #81Q10 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:81Q10

paper · pdf · doi:10.48550/arxiv.math-ph/0508023

arxiv created 2005/08/11 · arxiv updated 2009/12/01

Abstract

Consider a one dimensional quantum mechanical particle described by the Schroedinger equation on a closed curve of length 2π. 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 can not 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

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• An improved bound for the ground state of a Schrödinger operator on a loop

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