Semiclassical Quantization Rule for Bound-State Spectrum in Quantum Dots: Scattering Phase Approximation
凝聚态物理
2009-11-10 v3
摘要
We study the quantum propagator in the semiclassical limit with sharp confining potentials. Including the energy-dependent scattering phase due to sharp confining potential, the modified Van Vleck's formula is derived. We also discuss the close relations among quantum statistics, discrete gauge symmetry, and hard-wall constraints. Most of all, we formulate a new quantization rule that applies to {\it both} smooth and sharp boundary potentials. It provides an easy way to compute quantized energies in the semiclassical limit and is extremely useful for many physical systems.
引用
@article{arxiv.cond-mat/0303329,
title = {Semiclassical Quantization Rule for Bound-State Spectrum in Quantum Dots: Scattering Phase Approximation},
author = {Wei Chen and Tzay-Ming Hong and Hsiu-Hau Lin},
journal= {arXiv preprint arXiv:cond-mat/0303329},
year = {2009}
}
备注
REVTeX4, 6 pages, 3 figures, minor typos fixed and some references added