Remark on the uncertainty between angle and angular momentum

Franke-Arnold Franke-Arnold, Roberta Zambrini, S. S.Barnett +5 more

Jörg B. Götte, PAUL M. RADMORE, Roberta Zambrini +1 more

The uncertainty relation for angle and angular momentum has a lower bound which depends on the form of the state. Surprisingly, this lower bound can be very large. We derive the states which have the lowest possible uncertainty product for a given uncertainty in the angle or in the angular momentum. We show that, if the given angle uncertainty is close to its maximum value, the lowest possible uncertainty product tends to infinity.

Alvin Meckler

Jörg B. Götte, Roberta Zambrini, Sonja Franke‐Arnold +1 more

The equality in the uncertainty principle for linear momentum and position is obtained for states which also minimize the uncertainty product. However, in the uncertainty relation for angular momentum and angular position both sides of the inequality are state dependent and therefore the intelligent states, which satisfy the equality, do not necessarily give a minimum for the uncertainty product. In this paper, we highlight the difference between intelligent states and minimum uncertainty states by investigating a class of intelligent states which obey the equality in the angular uncertainty relation while having an arbitrarily large uncertainty product. To develop an understanding for the uncertainties of angle and angular momentum for the large-uncertainty intelligent states we compare exact solutions with analytical approximations in two limiting cases.

Jean-Marc Lévy-Leblond

Stephen P. Martin