David T Pegg et al 2005 New J. Phys. 7 62 doi:10.1088/1367-2630/7/1/062
Minimum uncertainty states of angular momentum and angular position
David T Pegg1, Stephen M Barnett2, Roberta Zambrini2,4, Sonja Franke-Arnold2 and Miles Padgett3
Show affiliationsThe states of linear momentum that satisfy the equality in the Heisenberg uncertainty principle for position and momentum, that is the intelligent states, are also the states that minimize the uncertainty product for position and momentum. The corresponding uncertainty relation for angular momentum and angular position, however, is more complicated and the intelligent states need not be the constrained minimum uncertainty product states. In this paper, we investigate the differences between the intelligent and the constrained minimum uncertainty product states for the angular case by means of instructive approximations, a numerical iterative search and the exact solution. We find that these differences can be quite significant for particular values of angular position uncertainty and indeed may be amenable to experimental measurement with the present technology.
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Issue 1 (February 2005)
Received 19 October 2004
Published 17 February 2005
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Minimum uncertainty states of angular momentum and angular position
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