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A Determination Methodology for the Evolution of Quantum Screened Coulomb Potential Systems at Fluctuationlessness Limit and the First Fluctuations in Expectation Value Evaluations

Last modified: 2020-01-22

#### Abstract

This work focuses on the determination of certain operators expectation values as temporal functions. Unless certain quite specific approximation methods are brought to the appications this is not a simple task. We prefer to deal with the expectation value ODEs to determine the measurable entities. The most facilitated issues in the determination of the certain operator's expectation values are perhaps the mathematical fluctuations. We focus on Screened Coulomb Potential Systems and then use the momentum and position as the basic operators. The first stage is the construction of ODEs for the determination of these two operator's expectation values as functions of time. The obtained relevant equations are first order ODEs whose right hand sides may not be multinomials in the expectation values of momentum and position, depending on the structure of the screening function in the potential which also has a singularity at the origin of the position whose values are only nonnegative. The space extension is used to get the multinomiality at the right hand sides as long as the screening function has appropriate specific structures to this end. Yukawa potential is brought to the scene for explanatory purpose. The resulting right hand sides are composed of certan expectation values which can be rather simplified to multinomials of the considered operators' expectation values at the fluctuationlessness limit. The first fluctuations are also evaluated within a rather methodological framework.