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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.