Chapter 6: Correlation Functions and Spectra

Using spectral method (see eig spectral HO M) to construct 2-D eigenstates. The movie below shows the wavefunction at different stages of formation, i.e. The Actual Formul for different accumulation times, The Actual Formul These wavefunctions were generated by forming a superposition of time evolving Gaussian wavepackets on the potential The Actual Formul and The Actual Formul Note that at short times the accumulated state looks like a superposition of all the places the moving wavepacket has visited. At longer times, however, the wavepacket returns multiple times to the same location. The ultimate nodal pattern of the wavefunction that is formed reflects the phase of the wavepacket as it returns in multiple passes, which in turn is governed by the classical action and topological phase of the wavepacket, as well as the energy at which the packet is Fourier transformed.