Some exactly solvable quantum-chaotic models

Exact analytical expressions are obtained for the wavefunctions of two atoms with a zero-range interaction in two types of the external potentials. The potential of first kind is a three-dimensional anisotropic harmonic oscillator; the second is a harmonic oscillator in two directions with periodic boundary conditions in the third direction. Neither of the two systems is known to possess a complete set of integrals of motion. The energy eigenvalues are roots of a transcendent equation and form a discrete spectrum. The energy spectrum statistics exhibits distinctive features of quantum-chaotic systems.