On the uncertainty relation for angle variables

Arthur A. Evett, Hormoz Mahmoud

Ernst Breitenberger

M. -C. Bouten, Norbert Maene, Piet Van Leuven

J.-P. Gazeau, T. Koide

Chandana Roy, A.B. Sannigrahi

Certain pitfalls regarding the uncertainty relation between angular momentum and the angle variable have been discussed from a didactical point of view. Further, an uncertainty relation has been derived for these variables in a simple and consistent manner; this relation is valid only for small values of uncertainty in the angle variable.

Sh. Tanimura

The uncertainty relation between angle and orbital angular momentum had not been formulated in a similar form as the uncertainty relation between position and linear momentum because the angle variable is not represented by a quantum mechanical self-adjoint operator.Instead of the angle variable operator, we introduce the complex position operator Ẑ = x + iŷ and interpret the order parameter µ = Ẑ / Ẑ † Ẑ as a measure of certainty of the angle distribution.We prove the relation between the uncertainty of angular momentum and the angle order parameter.We also prove its generalizations and discuss experimental methods for testing these relations.