# American Institute of Mathematical Sciences

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

## A fractal quantum mechanical model with Coulomb potential

 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.
Citation: Robert S. Strichartz. A fractal quantum mechanical model with Coulomb potential. Communications on Pure & Applied Analysis, 2009, 8 (2) : 743-755. doi: 10.3934/cpaa.2009.8.743
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