Initial Conditions of Closed Classical Orbits from Quantum Spectra

TL;DR

This paper introduces a method to extract initial conditions of classical closed orbits from quantum spectra of diamagnetic hydrogen, linking quantum spectral features to classical trajectory parameters.

Contribution

It presents a novel approach to determine classical orbit initial conditions directly from quantum spectral data using Fourier analysis and closed-orbit theory.

Findings

Successfully determines initial conditions of classical orbits from quantum spectra.

Shows the amplitude of spectral fluctuations correlates with classical orbit properties.

Provides a new way to connect quantum spectra with classical dynamics.

Abstract

A method is presented for determining the initial conditions of classical orbits from the quantum spectra of the diamagnetic hydrogen atom. Each classical trajectory which is closed at the nucleus produces a sinusoidal fluctuation in the photoabsorption spectrum. The amplitude of each orbit's contribution appears in the Fourier transform of a spectrum computed at constant scaled energy. For a given initial state, closed-orbit theory gives the dependence of this recurrence amplitude on the initial angle of an orbit. By comparing the recurrence amplitudes for different initial states, the initial conditions of closed classical orbits are determined from quantum spectra.