I outline two main themes that will be discussed. (1) I present some eigenfunctions for some quantum systems in a closed form. The classical systems corresponding to these systems are numerically found to be chaotic. The underlying reasoning is brought out by illustrating connections between some one-dimensional exactly solvable models involving many particles, and, billiards. (2) Comment will also be made on exactly solvable models in quantum mechanics when parity and time-reversal symmetries are broken. For these systems, random matrix studies point at different form for level repulsion.

Instituut voor Theoretische Fysica, Universiteit Utrecht