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Random Phases and Energy Dispersion |
| LIU Quan-Hui;LIU Tian-Gui;BAN Wei-Quan |
| School of Theoretical Physics and Department of Applied Physics, Hunan University, Changsha 410082 |
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LIU Quan-Hui, LIU Tian-Gui, BAN Wei-Quan 2003 Chin. Phys. Lett. 20 982-984 |
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Abstract Using 2N+1 successive stationary states centered at nth, we construct a rectangular wave packet in which the stationary states are superimposed with the equal weight √2N+1. With the requirement of the wave packet to be a quasi-classical state, the number N is determined by minimizing the uncertainty ΔxΔp. Since the stationary state can only be determined to within an arbitrary multiplicative complex phase factor of unit magnitude, a number of N is obtained as a set of the phases are given. For a harmonic oscillator, when all of the phase factors are essentially the same, we have N ≈ [61/3n2/3] with [x] signifying the integral part of positive number x. When every phase in the phase factors is given by a random number generated in a closed interval [0,2π] and when n ≥ 10, the probability of appearance of N is roughly 1/2N when N = 1 to 7, and does not exceed 0.01 when N ≥ 8.
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| Keywords:
03.65.Sq
03.75.Ca
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Published: 01 July 2003
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