Abstract
For a (classically) integrable quantum-mechanical system with two degrees of freedom, the functional dependence of the Hamiltonian operator on the action operators is analyzed and compared with the corresponding functional relationship in the classical limit of that system. The former converges toward the latter in some asymptotic regime associated with the classical limit, but the convergence is, in general, nonuniform. The existence of the function in the integrable regime of a parametric quantum system explains empirical results for the dimensionality of manifolds in parameter space on which at least two levels are degenerate. The analysis is carried out for an integrable one-parameter two-spin model. Additional results presented for the (integrable) circular billiard model illuminate the same conclusions from a different angle.
- Received 26 April 2000
DOI:https://doi.org/10.1103/PhysRevE.63.056202
©2001 American Physical Society