A quantum decay model with exact explicit analytical solution

TL;DR

This paper introduces an exactly solvable quantum decay model with a changing potential well, revealing non-exponential decay behavior and fractional power law decay at short times, challenging classical and perturbative quantum predictions.

Contribution

It presents a new quantum decay model with an exact analytical solution that captures non-classical decay dynamics and short-time fractional power law behavior.

Findings

Decay is never exponential, contrary to classical predictions.

Short-time decay follows a fractional power law.

Model provides exact solutions for quantum decay processes.

Abstract

A simple decay model is introduced. The model comprises of a point potential well, which experiences an abrupt change. Due to the temporal variation the initial quantum state can either escape from the well or stay localized as a new bound state. The model allows for an exact analytical solution while having the necessary features of a decay process. The results show that the decay is never exponential, as classical dynamics predicts. Moreover, at short times the decay has a \textit{fractional} power law, which differs from perturbation quantum methods predictions.