Asymptotic form of the penetration probability of the quantum harmonic oscillator into the classically forbidden region
作者:
D. E. Atems,
J. M. Wadehra,
期刊:
American Journal of Physics
(AIP Available online 1995)
卷期:
Volume 63,
issue 5
页码: 443-446
ISSN:0002-9505
年代: 1995
DOI:10.1119/1.17908
出版商: American Association of Physics Teachers
关键词: QUANTUM MECHANICS;QUANTUM NUMBERS;HARMONIC OSCILLATORS;ASYMPTOTIC SOLUTIONS;EIGENFUNCTIONS
数据来源: AIP
摘要:
The penetration probability of the quantum harmonic oscillator into the classically forbidden region is examined in the limit of large quantum numbers using analytical methods. An expression is derived for the asymptotic form of the penetration probability, and is shown to be in good agreement with an earlier result obtained by numerical methods. The asymptotic form of the probability density in the region between the classical turning points is also presented and found to have a simple physical interpretation.
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