Tutorial on Time-dependent Quantum Mechanics
Sunday, January 11, 2009 - 3:30pm - 5:30pm
Many people find time-dependent quantum mechanics the most interesting and understandable part of quantum mechanics. However, standard courses in quantum mechanics devote little attention to this perspective, and its relationship to the rest of the syllabus is disjointed. Yet it is possible to develop quantum mechanics from beginning to end from a time-dependent perspective, using a small set of conceptual building blocks. The tutorial will have two parts. In the first part I will present the basic building blocks. I will begin with several animations that highlight the visual appeal of time-dependent quantum mechanics and its relationship with classical mechanics. Next, I will introduce the concept of a wavepacket time-correlation function and show how it is related to a spectrum via Fourier transform. I will then discuss the reciprocity of wavepackets and eigenstates — just as a wavepacket is a superposition of eigenstates, an eigenstate is a superposition of wavepackets. Finally, I will return to wavepacket time-correlation functions and show how they can be used to calculate reflection/transmission probabilities, emphasizing that barrier scattering and spectroscopy are two sides of the same coin. In the second part of the tutorial I will show that the time-dependent perspective provides a simple and unified interpretation of many of the frontier experiments in modern Chemical Physics — from femtochemistry to resonance Raman spectroscopy, from coherent control to photodissociation to reactive scattering — using the same small set of conceptual building blocks described in the first part.