Complex Correspondence Principle

TL;DR

This paper demonstrates that the correspondence principle between quantum and classical mechanics extends into the complex domain, with the relationship becoming more evident through advanced asymptotic analysis.

Contribution

It reveals that complex quantum and classical mechanics maintain a correspondence, using asymptotics beyond all orders to demonstrate this subtle relationship.

Findings

Complex extensions of quantum and classical mechanics exhibit a correspondence.

The correspondence becomes more pronounced in the complex domain.

Asymptotics beyond all orders are necessary to demonstrate the relationship.

Abstract

Quantum mechanics and classical mechanics are two very different theories, but the correspondence principle states that quantum particles behave classically in the limit of high quantum number. In recent years much research has been done on extending both quantum mechanics and classical mechanics into the complex domain. This letter shows that these complex extensions continue to exhibit a correspondence, and that this correspondence becomes more pronounced in the complex domain. The association between complex quantum mechanics and complex classical mechanics is subtle and demonstrating this relationship prequires the use of asymptotics beyond all orders.