On the Time-Dependent Analysis of Gamow Decay

TL;DR

This paper explores the compatibility of Gamow's exponential decay model with standard quantum mechanics, providing a clear, accessible analysis suitable for educational purposes.

Contribution

It offers a straightforward, pedagogical approach to understanding how Gamow's complex eigenvalues relate to real eigenvalues in quantum decay processes.

Findings

Clarifies the role of generalized eigenfunctions in decay

Reconciles Gamow's model with standard quantum theory

Provides educational insights into quantum decay analysis

Abstract

Gamow's explanation of the exponential decay law uses complex "eigenvalues" and exponentially growing "eigenfunctions". This raises the question, how Gamow's description fits into the quantum mechanical description of nature, which is based on real eigenvalues and square integrable wave functions. Observing that the time evolution of any wave function is given by its expansion in generalized eigenfunctions, we shall answer this question in the most straightforward manner, which at the same time is accessible to graduate students and specialists. Moreover the presentation can well be used in physics lectures to students.