Quantum jumps and classical harmonics

Abstract

We present an introduction to quantum mechanics based on the formal correspondence between the atomic properties of quantum jumps and the classical harmonics of the electron’s periodic motion. By adding a simple quantum condition to the classical Fourier analysis, we readily find the energies of the stationary states, calculate the transition probabilities between the states, and construct the line spectrum of the emitted light. We provide examples to illustrate the asymptotic, and sometimes exact, agreement between the classical-quantum results (Fourier harmonics) and the exact quantum results (Heisenberg harmonics).