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Probability uncertainty of quantal objects.

Vladimír Majerník

Published Jan 1, 1972• 0 citations
OpenAlex

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Progress of Theoretical Physics•Oct 1, 1992•1 citation
The authors examine the effect of the Coulomb singularity on the classical and semiclassical dynamics of the one-dimensional model for atomic hydrogen, sometimes called the surface-state-electron model, in a periodic electric field and determine a necessary condition, in terms of the field strength, frequency and the initial quantum number, for the violation of the uncertainty principle. They show that when this violation occurs the quantal transition probabilities are significantly less than the equivalent classical probabilities. This criterion is tested numerically and shown to provide a good estimate of the boundary to one of the regions in which classical dynamics fails. The authors also show that when the uncertainty principle is not violated the fluctuations of the quantal about the classical probability spectra can be related to structure in classical phase space. These fluctuations are due to different classical and quantal transport through cantori.
A viewpoint for describing time development of wave packet with the least quantal effect is proposed in the case of system obeying the su(2)-algebra, i.e., the quasi-spin. The basic idea is a possible extension of a method developed by the present authors, together with Tsue and Fujiwara, for one-dimensional system. Concerning the least quantal effect, the uncertainty relations coming from the non-commutability among the components of the quasi-spin are investigated and a certain condition for the least quantal effect in the quasi-spin is presented.
A viewpoint for describing time development of wave packet with the least quantal effect is proposed in the case of system obeying the su(2)-algebra, i.e., the quasi-spin. The basic idea is a possible extension of a method developed by the present authors, together with Tsue and Fujiwara, for one-dimensional system. Concerning the least quantal effect, the uncertainty relations coming from the non-commutability among the components of the quasi-spin are investigated and a certain condition for the least quantal effect in the quasi-spin is presented.