A FRACTAL QUANTUM MECHANICAL MODEL WITH COULOMB POTENTIAL

被引：13

作者：

Strichartz, Robert S. ^{[1
]}

机构：

[1] Cornell Univ, Dept Math, Ithaca, NY 14853 USA

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2009年 / 8卷 / 02期

基金：

美国国家科学基金会;

关键词：

Analysis on fractals; Sierpinski gasket; Schrodinger operator with Coulomb potential; nonrelativistic Hydrogen atom model; METRIC MEASURE-SPACES; BROWNIAN-MOTION; SIERPINSKI CARPETS; HARNACK INEQUALITIES; GASKET;

D O I：

10.3934/cpaa.2009.8.743

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the Schrodinger 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.

引用

页码：743 / 755

页数：13

共 27 条

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[2]

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[3]

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