Unitarity of quantum tunneling decay for an analytical exact non-Hermitian resonant-state approach

TL;DR

This paper demonstrates that unitarity is preserved in quantum tunneling decay processes when using an exact non-Hermitian formalism with resonance states, providing a fundamental understanding of quantum decay.

Contribution

It introduces an exact analytical non-Hermitian approach that confirms unitarity in quantum tunneling decay using resonance states and complex energy eigenvalues.

Findings

Unitarity holds at all times in quantum tunneling decay.

The formalism involves the full set of resonance (quasinormal) states.

Provides a fundamental description of quantum decay processes.

Abstract

By using an exact analytical non-Hermitian formalism involving the full set of resonance (quasinormal) states and complex energy eigenvalues for quantum tunneling decay, we show that unitarity holds at any instant of time for the nonstationary decaying probability density in the whole space, thus providing a fundamental description of the quantum mechanical decay process.