Displacement operators: the classical face of their quantum phase

In quantum mechanics, the operator representing the displacement of a system in position or momentum is always accompanied by a path-dependent phase factor. In particular, two non-parallel displacements in phase space do not compose together in a simple way, and the order of these displacements leads to different displacement composition phase factors. These phase factors are often attributed to the nonzero commutator between quantum position and momentum operators, but such a mathematical explanation might be unsatisfactory to students who are after more physical insight. We present a couple of simple demonstrations, using classical wave mechanics and classical particle mechanics, that provide some physical intuition for the phase associated with displacement operators.Comment: 14 pages, 4 figures, reorganized and reformatte

ON ROUGH I∗I^* AND IKI^K-CONVERGENCE OF SEQUENCES IN NORMED LINEAR SPACES

In this paper, we have introduced first the notion of rough $I^*$-convergence in a normed linear space as an extension work of rough $I$-convergence and then rough $I^K$-convergence in more general way. Then we have studied some properties on these two newly introduced ideas. We also examined the relationship between rough $I$-convergence with both of rough $I^*$-convergence and rough $I^K$-convergence

The citrate cleavage enzyme. III. Citryl coenzyme a as a substrate and the stereospecificlty of the enzyme

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On rough I∗I^* and IKI^K-convergence of sequences in normed linear spaces

In this paper, we have introduced first the notion of rough $I^*$-convergence in a normed linear space as an extension work of rough $I$-convergence and then rough $I^K$-convergence in more general way. Then we have studied some properties on these two newly introduced ideas. We also examined the relationship between rough $I$-convergence with both of rough $I^*$-convergence and rough $I^K$-convergence.Comment: 13 page