Quantum and semiclassical scales for the x sup n anharmonic oscillator

Journal Article · Sat Mar 21 04:00:00 EST 1992 · Modern Physics Letters A; (United States)

DOI:https://doi.org/10.1142/S0217732392000732· OSTI ID:5298645

Anderson, J T ^[1]

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1. Mathematics Dept., State Univ. of New York, Stony Brook, NY (US)

This paper reports that the classical fine structure around a singular point has been shown to be smoothed out by {Dirac h} in quantum mechanics. For the x{sup n} anharmonic oscillator in the semiclassical approximation this results is shown to set a quantum length scale x{sup 2}{sub 0} = h/mw{sub a} below which the fine structure is not observable. The length scale allows canonical quantization in terms of the ratio of the quantum to semiclassical scales x{sup 2}{sub 0}/x{sup 2}{sub cl}. This ratio is equivalent to ratios of the quantum to semiclassical scales in action and energy and provides a measure of the departure of semiclassical from quantum invariants.

• OSTI ID: 5298645
• Journal Information: Modern Physics Letters A; (United States), Journal Name: Modern Physics Letters A; (United States) Vol. 7:9; ISSN 0217-7323; ISSN MPLAE
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANHARMONIC OSCILLATORS
CANONICAL DIMENSION
ELECTRONIC EQUIPMENT
EQUIPMENT
FINE STRUCTURE
INVARIANCE PRINCIPLES
MECHANICS
OSCILLATORS
PLANCK LAW
QUANTIZATION
QUANTUM MECHANICS
SCALE DIMENSION
SEMICLASSICAL APPROXIMATION
SINGULARITY