Resonance wave functions located at the Stark saddle point

TL;DR

This paper demonstrates the existence of long-lived quantum resonance states localized at the Stark saddle point in a hydrogen atom subjected to crossed external fields, confirmed through exact quantum calculations.

Contribution

It provides the first quantum mechanical proof of resonance wave functions localized at the Stark saddle point, validating simple potential approximations.

Findings

Identification of resonance states near the saddle point

Confirmation of nodal patterns matching quadratic and cubic potential expansions

Evidence of long-lived decaying quantum states at the saddle

Abstract

We calculate quantum mechanically exact wave functions of resonances in spectra of the hydrogen atom in crossed external fields and prove the existence of long-lived decaying quantum states localized at the Stark saddle point. A spectrum of ground and excited states reproducing the nodal patterns expected from simple quadratic and cubic expansions of the potential in the vicinity of the saddle point can be identified. The results demonstrate the presence of resonances in the vicinity of the saddle predicted by simple approximations.