This article aims to calculate the strict quantum transition rate and points out that the Fermi Golden Rule is the result of its “long-time average”. The strict quantum transition rate contains an additional double-frequency oscillation term with non-negligible amplitude compared to the Fermi Golden Rule. The relationship between the two is similar to “instantaneous power” and “average power” in AC circuits.

This note is approximately 10,000 words long and aims to help readers get started with Fractional Quantum Hall Effect (FQHE), Fractional Anomalous Quantum Hall Effect (FAQHE), and Fractional Chern Insulators (FCI). This article represents only my personal perspective and may contain errors; I welcome corrections from readers. Below is the main text.