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Semiclassical Quantization Rule for Bound-State Spectrum in Quantum Dots: Scattering Phase Approximation

Wei Chen·Tzay-Ming Hong·Hsiu-Hau Lin
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Abstract

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.

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Wei Chen, Tzay-Ming Hong, Hsiu-Hau Lin. 2003-06-19. Semiclassical Quantization Rule for Bound-State Spectrum in Quantum Dots: Scattering Phase Approximation. https://doi.org/10.1103/physrevb.68.205104

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