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UNCERTAINTY RELATIONS FOR THE TIME-DEPENDENT SINGULAR OSCILLATOR

J. R. CHOI

Department of Physics and Advanced Materials Science, Sun Moon University, Asan 336-708, Republic of Korea

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and

I. H. NAHM

Department of Physics and Advanced Materials Science, Sun Moon University, Asan 336-708, Republic of Korea

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https://doi.org/10.1142/S0217979206033802Cited by:1 (Source: Crossref)

Abstract

Uncertainty relations for the time-dependent singular oscillator in the number state and in the coherent state are investigated. We applied our developement to the Caldirola–Kanai oscillator perturbed by a singularity. For this system, the variation (Δx) decreased exponentially while (Δp) increased exponentially with time both in the number and in the coherent states. As k → 0 and χ → 0, the number state uncertainty relation in the ground state becomes 0.583216ℏ which is somewhat larger than that of the standard harmonic oscillator, ℏ/2. On the other hand, the uncertainty relation in all excited states become smaller than that of the standard harmonic oscillator with the same quantum number n. However, as k → ∞ and χ → 0, the uncertainty relations of the system approach the uncertainty relations of the standard harmonic oscillator, (n+1/2)ℏ.

Keywords:

PACS: 03.65.Ge, 03.65.-w

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