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A fractal quantum mechanical model with Coulomb potential

2008; American Institute of Mathematical Sciences; Volume: 8; Issue: 2 Linguagem: Inglês

10.3934/cpaa.2009.8.743

1553-5258

Robert S. Strichartz,

Statistical Mechanics and Entropy

We study the Schrödinger operator $ H = - \Delta + V $ on theproduct of two copies of an infinite blowup of the Sierpinski gasket,where $ V$ is the analog of a Coulomb potential ($\Delta V$ is amultiple of a delta function). So $H$ is the analog of the standardHydrogen atom model in nonrelativistic quantum mechanics. Like theclassical model, we show that the essential spectrum of $H$ is thesame as for $ - \Delta $, and there is a countable discrete spectrumof negative eigenvalues.