In: Geometry, Integrability and Quantization V
(Proceedings of Int. Conference,Softex,  Sofia 2004),
pp 211-224 (http://www.bio21.bas.bg/proceedings/)
[E-print  quant-ph/0404087]
 

POSITION UNCERTAINTY MEASURES ON THE SPHERE

DIMITAR  A.  TRIFONOV

Institute for Nuclear Research and Nuclear Energy,
Bulgarian Academy of Sciences
72 Tzarigradsko chaussee  Blvd,1784 Sofia, Bulgaria
 

Abstract.Position uncertainty (delocalization) measures for a particle on
the sphere are proposed and illustrated on several examples of states. The
new measures are constructed using suitably the standard multiplication angle
operator variances. They are shown to depend solely on the state of the
particle and to obey uncertainty relations of the Schroedinger-Robertson type.
A set of Hermitian operators with continuous spectrum is pointed out the
variances of which are complementary to the longitudinal angle uncertainty
measure.