Applications of Lie systems in quantum mechanics and control theory
Volume 59 / 2003
Banach Center Publications 59 (2003), 143-162
MSC: Primary 34A26; Secondary 81Q70, 93B29.
DOI: 10.4064/bc59-0-7
Abstract
Some simple examples from quantum physics and control theory are used to illustrate the application of the theory of Lie systems. We will show, in particular, that for certain physical models both of the corresponding classical and quantum problems can be treated in a similar way, may be up to the replacement of the Lie group involved by a central extension of it. The geometric techniques developed for dealing with Lie systems are also used in problems of control theory. Specifically, we will study some examples of control systems on Lie groups and homogeneous spaces.
