CONSTRAINT OPERATOR SOLUTION TO QUANTUM BILLIARD PROBLEMS

We introduce an additional method to solve Schrodinger'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 contai n the wave function to a region within the domain of the basis functio ns. In this manner, a quantum billiard problem of arbitrary shape can be solved. Several methods exist to solve problems of this sort, but a s recent work reviewing these methods has shown, all have shortcomings . Our work represents a different direction in the solution of these p roblems. Our method is different in that it provides a means of comput ing an eigenbasis. It is also interesting from a physical standpoint i n that it can represent the Hamiltonian of a classically chaotic syste m in the basis of a classically regular system.