Semiclassical methods for multi-dimensional systems bounded by finite potentials

TL;DR

This paper improves semiclassical methods for multi-dimensional quantum systems with finite potentials by replacing the Maslov index with a scattering phase, leading to more accurate energy calculations.

Contribution

It introduces a modified transfer operator method using a scattering phase, enhancing semiclassical approximations for finite potential systems.

Findings

Accurate quantum energy corrections for finite potential wells.

Validation of the scattering phase correction approach.

Potential to improve other semiclassical methods.

Abstract

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.