  We study classical and quantum dynamics of two spinless particles confined in
a quantum wire with repulsive or attractive Coulomb interaction. The
interaction induces irregular dynamics in classical mechanics, which reflects
on the quantum properties of the system in the energy level statistics (the
signatures of quantum chaos). We investigate especially closer correspondence
between the classical and quantum chaos. The present classical dynamics has
some scaling property, which the quantum counterpart does not have. However, we
demonstrate that the energy level statistics implies the existence of the
corresponding scaling property even in the quantum system. Instead of ordinary
maximum Lyapunov exponent (MLE), we introduce a novel kind of MLE, which is
shown to be suitable measure of chaotic irregularity for the present classical
system. We show that tendency of the energy dependence of the Brody parameter,
which characterizes the energy level statistics in the quantum system, is
consistent with that of the novel kind of MLE.
