MSI Weekly Bulletin - Week starting Monday 19 February, 2007

see web address http://wwwmaths.anu.edu.au/events/hda07/program07.html for further Program Details

If you are going to be involved in teaching a 3rd or 4th year course (standard or not) in either semester, please be at the meeting and please be prepared to say a few words about your course. Besides giving you a good opportunity to advertise your course, it is also where you can arrange the time and place of the first meeting of the course.

see web link http://wwwmaths.anu.edu.au/events/hda07/program07.html for program details

see web link http://wwwmaths.anu.edu.au/events/hda07/program07.html for program details

see web link http://wwwmaths.anu.edu.au/events/hda07/program07.html for program details

With the work of Schršdinger and Heisenberg in 1926, quantum mechanics found its final form and the complete mathematical description of atoms and molecules had become possible. Dirac commented this with the words "The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble.'' The reason is the high dimensionality of the Schršdinger equation. Its solutions depend on 3N variables for a system consisting of N particles, three spatial coordinates for each particle. Although very sophisticated and highly successful simplified models accessible to a numerical treatment have been developed during the last decades forming the basis of a whole branch of chemistry, from a mathematical point of view the situation has not much changed since Dirac's time. It is shown in this talk how a refined regularity theory for the electronic Schršdinger equation and modern principles of approximation theory and numerical analysis could help to change this situation and why the construction of true numerical methods for the Schršdinger equation could come into reach now.