Coordinate Realizations of Deformed Lie Algebras with Three Generators
R. Dutt, A. Gangopadhyaya, C. Rasinariu, U. Sukhatme
TL;DR
This paper develops coordinate space differential realizations for deformed Lie algebras with three generators using bosonic operators, unifying previous results and applying them to quantum mechanics eigenvalue problems.
Contribution
It provides a unified framework for coordinate realizations of various deformed Lie algebras with three generators, including all known special cases.
Findings
Unified treatment of deformed Lie algebra realizations
Application to eigenvalue problems in quantum mechanics
Extension of previous coordinate realization methods
Abstract
Differential realizations in coordinate space for deformed Lie algebras with three generators are obtained using bosonic creation and annihilation operators satisfying Heisenberg commutation relations. The unified treatment presented here contains as special cases all previously given coordinate realizations of and their deformations. Applications to physical problems involving eigenvalue determination in nonrelativistic quantum mechanics are discussed.
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