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March  2009, 8(2): 743-755. doi: 10.3934/cpaa.2009.8.743

A fractal quantum mechanical model with Coulomb potential

Robert S. Strichartz 1,

1. 

Mathematics Department, Malott Hall, Cornell Univeristy, Ithaca, NY 14853, United States

Received  March 2008 Revised  July 2008 Published  December 2008

We study the Schrödinger operator $ H = - \Delta + V $ on the product of two copies of an infinite blowup of the Sierpinski gasket, where $ V$ is the analog of a Coulomb potential ($\Delta V$ is a multiple of a delta function). So $H$ is the analog of the standard Hydrogen atom model in nonrelativistic quantum mechanics. Like the classical model, we show that the essential spectrum of $H$ is the same as for $ - \Delta $, and there is a countable discrete spectrum of negative eigenvalues.
Keywords: Schrödinger operator with Coulomb potential, nonrelativistic Hydrogen atom model, Analysis on fractals, Sierpinski gasket.
Mathematics Subject Classification: Primary: 28A80, 35J10, 35Q40, 81Q05.
Citation: Robert S. Strichartz. A fractal quantum mechanical model with Coulomb potential. Communications on Pure and Applied Analysis, 2009, 8 (2) : 743-755. doi: 10.3934/cpaa.2009.8.743
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