Study of Gamow States in the Rigged Hilbert Space with Tempered Ultradistributions

TL;DR

This paper extends the mathematical framework for Gamow states using tempered ultradistributions, allowing a broader class of states to be analyzed, exemplified by s-states in a square well potential.

Contribution

It introduces an analytical extension of the pseudonorm for Gamow states via tempered ultradistributions, applicable to states from zeros of the Jost function.

Findings

Extended the pseudonorm to all states from Jost function zeros

Applied the framework to s-states in a square well potential

Demonstrated the mathematical consistency of the extension

Abstract

In this work we show that it is possible to extend analitically, and with the use of tempered ultradistributions, the pseudonorm defined by T. Berggren for Gamow states. We define this pseudonorm for all states determined by the zeros of the Jost function for any short range potential. As an example we study the s-states corresponding to the square well potential.