Abstract
We study the most elementary aspects of harmonic analysis on a homogeneous space of a deformation of the two-dimensional Euclidean group, admitting generalizations to dimensions three and four, whose quantum parameter has the physical dimensions of length. The homogeneous space is recognized as a new quantum plane and the action of the Euclidean quantum group is used to determine an eigenvalue problem for the Casimir operator, which constitutes the analogue of the Schrodinger equation in the presence of such a deformation. The solutions are given in the plane-wave and angular-momentum bases and are expressed in terms of hypergeometric series with non-commuting parameters.
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