1/n Expansion of Resonant States

TL;DR

This paper introduces a general analytic method to expand resonant states in quantum systems using powers of 1/n, providing explicit formulas for certain potential barrier models.

Contribution

It develops a novel 1/n expansion technique for resonant states, offering explicit formulas for specific quantum potential models.

Findings

Derived explicit formulas for resonant states in potential barrier models

Established a general 1/n expansion framework for quantum resonances

Enhanced analytical understanding of quantum resonant states

Abstract

We present a general analytic expansion in powers of $1/n$ of the resonant states of quantum-mechanical systems, where $n=1,2,3,\cdots$ is the excitation number. Explicit formulas are obtained for some potential barrier models.