Positive Fractal Dimensions of Bound States Spectral Measures: Application to the Hydrogen Atom

被引：0
|
作者：
Aloisio, Moacir [1 ]
Carvalho, Silas L. [2 ]
de Oliveira, Cesar R. [3 ]
机构：
[1] Univ Fed Amazonas, Dept Matemat, BR-69067005 Manaus, Amazonas, Brazil
[2] Univ Fed Minas Gerais, Dept Matemat, BR-30161970 Belo Horizonte, MG, Brazil
[3] Univ Fed Sao Carlos, Dept Matemat, BR-13560970 Sao Carlos, SP, Brazil
来源：
BRAZILIAN JOURNAL OF PHYSICS | 2022年 / 52卷 / 02期
关键词：
Hydrogen atom; Bound states; Generalized dimensions; Spectral measures; GENERALIZED DIMENSIONS; QUANTUM; OPERATORS; TRANSPORT;
D O I：
10.1007/s13538-021-01037-9
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
It is shown that generically, in Baire's sense, the bound states of the Hamiltonian of the hydrogen atom have spectral measures with exact 0-lower and 1/3-upper generalized fractal dimensions; the relation to (a weak form of) dynamical delocalization along orthonormal bases is also discussed. Such result is a consequence of certain distributions of the Hamiltonian eigenvalues for which the hydrogen atom is a particular case.
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页数：8
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