Bound state eigenfunctions from wave packets: Time→energy resolution

Abstract

We present a method to obtain bound-state eigenfunctions in any arbitrary range of energies, by a Fourier resolution (from time to energy) of a real-time wave packet. The resolution is done simultaneously at a number of energies within the sought range, and the resulting vectors yield, after diagonalization, all bound-state eigenvalues and eigenfunctions within that range. The method is exemplified on a Morse potential: eigenfunctions for 18 high-lying states (n∼200) are obtained from resolution at 25 energies.