Quantum mechanics on space with SU(2) fuzziness

TL;DR

This paper explores quantum mechanics on spaces with SU(2) noncommutative geometry, deriving eigenvalue problems and analyzing invariant systems, thus extending quantum models to fuzzy spaces with Lie algebraic structures.

Contribution

It introduces a formulation of quantum mechanics on SU(2)-fuzzy spaces using Euler parameterization, providing a method to analyze invariant systems and reduce eigenvalue problems.

Findings

Eigenvalue problem reduced to ordinary differential equation

Formulation applicable to SU(2)-invariant quantum systems

Extension of quantum mechanics to noncommutative SU(2) spaces

Abstract

Quantum mechanics of models is considered which are constructed in spaces with Lie algebra type commutation relations between spatial coordinates. The case is specialized to that of the group SU(2), for which the formulation of the problem via the Euler parameterization is also presented. SU(2)-invariant systems are discussed, and the corresponding eigenvalue problem for the Hamiltonian is reduced to an ordinary differential equation, as it is the case with such models on commutative spaces.