Zero-Energy Quantum States for a Class of Noncentral Potentials and an Exact Classical Limit

摘要

We extend results of the recent paper by Kobayashi and Shimbori [Phys. Rev. A65, 042108 (2002)] to a large class of noncentral potentials. Namely, we have shown that zero-energy states of the central potentials considered by these Authors [V _a(ρ) = ?a²g_aρ^2(a?1) with ρ = √x² + y² and a≠0] and noncentral potentials discussed here, have both common set of solutions given by wave functions of the parabolic potential barrier (PPB). Moreover, it is observed that first few members of the infinite set of functions cancel the quantum correction to the classical Hamilton–Jacobi equation. The exact classical limit of quantum mechanics is thus precisely reached for them with no approximation involved.