Abstract
Two-dimensional central potentials leading to the identical classical and quantum motions are derived and their properties are discussed. Some of zero-energy states in the potentials are shown to cancel the quantum correction to the classical Hamilton-Jacobi equation. The Bohr’s correspondence principle is thus fulfilled exactly without taking the limits of high quantum numbers, of or of the like. In this exact limit of classical trajectories are found and classified. Interestingly, many of them are represented by closed curves. Applications of the found potentials in many areas of physics are briefly commented.
- Received 13 August 2002
DOI:https://doi.org/10.1103/PhysRevA.66.062103
©2002 American Physical Society