Semiclassical methods for multi-dimensional systems bounded by finite potentials

Details Semiclassical methods for multi-dimensional systems bounded by finite potentials Semiclassical methods for multi-dimensional systems bounded by finite potentials

2004-12-13

arxiv.org/abs/cond-mat/0412326v2

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 4 figures

Scientific paper

This work studies the semiclassical methods in multi-dimensional quantum systems bounded by finite potentials. By replacing the Maslov index by the scattering phase, the modified transfer operator method gives rather accurate corrections to the quantum energies of the circular and square potential pots of finite heights. The result justifies the proposed scattering phase correction which paves the way for correcting other semiclassical methods based on Green functions, like Gutzwiller trace formula, dynamical zeta functions, and Landauer-B\"uttiker formula.

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