Bohr's correspondence principle: The cases for which it is exact

Journal Article · Sun Dec 01 00:00:00 EST 2002 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.66.062103· OSTI ID:20632398

Makowski, Adam J; Gorska, Katarzyna J ^[1]

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1. Institute of Physics, Nicholas Copernicus University, ul.Grudziadzka 5/7, 87-100 Torun (Poland)

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 Q=(-({Dirac_h}/2{pi}){sup 2}/2m){delta}R/R to the classical Hamilton-Jacobi equation. The Bohr's correspondence principle is thus fulfilled exactly without taking the limits of high quantum numbers, of ({Dirac_h}/2{pi}){yields}0, or of the like. In this exact limit of Q=0, 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.

• OSTI ID: 20632398
• Journal Information: Physical Review. A, Vol. 66, Issue 6; Other Information: DOI: 10.1103/PhysRevA.66.062103; (c) 2002 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
CENTRAL POTENTIAL
CORRECTIONS
DIAGRAMS
HAMILTON-JACOBI EQUATIONS
QUANTUM NUMBERS
TRAJECTORIES
TWO-DIMENSIONAL CALCULATIONS
USES