Constraint operator solution to quantum billiard problems.

We introduce an additional method to solve Schrödinger’s equation for a free particle in an infinite well of arbitrary shape ~the Helmholtz equation with Dirichlet boundary conditions!, a problem of interest in the area of quantum chaos. We expand the wave function in a basis of products of sine functions, then use the constraint operator to contain the wave function to a region within the domain of the basis functions. In this manner, a quantum billiard problem of arbitrary shape can be solved. Several methods exist to solve problems of this sort, but as recent work reviewing these methods has shown, all have shortcomings. Our work represents a different direction in the solution of these problems. Our method is different in that it provides a means of computing an eigenbasis. It is also interesting from a physical standpoint in that it can represent the Hamiltonian of a classically chaotic system in the basis of a classically regular system. @S1063-651X~96!06607-X#