318 research outputs found
Schwinger, Pegg and Barnett and a relationship between angular and Cartesian quantum descriptions
From a development of an original idea due to Schwinger, it is shown that it
is possible to recover, from the quantum description of a degree of freedom
characterized by a finite number of states (\QTR{it}{i.e}., without classical
counterpart) the usual canonical variables of position/momentum \QTR{it}{and}
angle/angular momentum, relating, maybe surprisingly, the first as a limit of
the later.Comment: 7 pages, revised version, to appear on J. Phys. A: Math and Ge
Quasiprobability distribution functions for periodic phase-spaces: I. Theoretical Aspects
An approach featuring -parametrized quasiprobability distribution
functions is developed for situations where a circular topology is observed.
For such an approach, a suitable set of angle-angular momentum coherent states
must be constructed in appropriate fashion.Comment: 13 pages, 3 figure
Schwinger, Pegg and Barnett approaches and a relationship between angular and Cartesian quantum descriptions II: Phase Spaces
Following the discussion -- in state space language -- presented in a
preceding paper, we work on the passage from the phase space description of a
degree of freedom described by a finite number of states (without classical
counterpart) to one described by an infinite (and continuously labeled) number
of states. With that it is possible to relate an original Schwinger idea to the
Pegg and Barnett approach to the phase problem. In phase space language, this
discussion shows that one can obtain the Weyl-Wigner formalism, for both
Cartesian {\em and} angular coordinates, as limiting elements of the discrete
phase space formalism.Comment: Subm. to J. Phys A: Math and Gen. 7 pages, sequel of quant-ph/0108031
(which is to appear on J.Phys A: Math and Gen
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