Australian Mathematical Society
Mathematics Department at Macquarie University

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50th Annual Meeting of the Australian Mathematical Society

Plenary Talk in Macquarie Theatre

Wednesday 27 September 2006 at 08:45


Andrew Hassell (Australian National University)


The Time-Dependent Schrödinger Equation


One of the most powerful strategies for understanding solutions of linear partial differential equations is to analyse the fundamental solution as precisely as possible. In this lecture I will consider the fundamental solution of the time-dependent Schrödinger equation, usually known as the "propagator".

In contrast to the situation with the heat or wave equations, where the fundamental solutions have been well-understood for decades, the propagator has only recently been precisely analysed, and then only in certain special geometrical situations. In this lecture, drawing on some joint work of mine with Wunsch, and with Tao and Wunsch, I will describe some properties of the propagator when the domain is an asymptotically conic, nontrapping manifold (a generalization of Euclidean space), and give some applications.