Angular Momentum and Mutually Unbiased Bases
Abstract
The Lie algebra of the group SU(2) is constructed from two deformed oscillator algebras for which the deformation parameter is a root of unity. This leads to an unusual quantization scheme, the J2,Ur scheme, an alternative to the familiar J2,Jz quantization scheme corresponding to common eigenvectors of the Casimir operator J2 and the Cartan operator Jz. A connection is established between the eigenvectors of the complete set of commuting operators J2,Ur and mutually unbiased bases in spaces of constant angular momentum.
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