Quantum Mechanics on Laakso Spaces

Details Quantum Mechanics on Laakso Spaces Quantum Mechanics on Laakso Spaces

2010-11-16

arxiv.org/abs/1011.3567v2

Mathematics

Classical Analysis and ODEs

v2: Updated and revised text from preliminary report. v1:Preliminary Report from a Summer 2010 REU at the University of Connec

Scientific paper

We first review the spectrum of the Laplacian operator on a general Laakso Space before considering modified Hamiltonians for the infinite square well, parabola, and Coulomb potentials. Additionally, we compute the spectrum for the Laplacian and its multiplicities when certain regions of a Laakso space are compressed or stretched and calculate the Casimir force experienced by two uncharged conducting plates by imposing physically relevant boundary conditions and then analytically regularizing the result. Lastly, we derive a general formula for the spectral zeta function and its derivative for Laakso spaces with strict self-similar structure before listing explicit spectral values for cases of interest.

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