Non-Separable Variables: Hierarchical Quantization and Tunneling Resonances
The study of an electron in a co-focal elliptic shell is very instructive. In classical mechanics its motion is chaotic. In quantum mechanics variables are separable in the absence of magnetic field. Then the energy spectrum is readily determined. When the interfocal distance d infinitely increases, while the shell width is kept finite, the spectrum above a mobility edge energy E n consists of intersecting branches (n is the branch number). Lower energy states E < E n are localized in the widest region .
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