INVERSE SQUARE PROBLEM AND so(2, 1) SYMMETRY IN NONCOMMUTATIVE SPACE

Abstract

We study the quantum mechanics of a system with inverse square potential in noncommutative space. Both the coordinates and momenta are considered to be noncommutative, which breaks the original so(2, 1) symmetry. The energy levels and eigenfunctions are obtained. The generators of the so(2, 1) algebra are also studied in noncommutative phase space and the commutators are calculated, which shows that the commutators obtained in noncommutative space is not closed. However the commutative limit Θ, [Formula: see text] for the commutators smoothly go to the standard so(2, 1) algebra.

Falling of a quantum particle in an inverse square attractive potential

“…Also bound states for an inverse square potential may appear within the renormalization scheme [11], [12]. It is interesting that an inverse square potential is regularized in a natural way in a space with a minimal length [13] and noncommutative space [14]. In all these methods an additional parameter with the dimension of length appears, which is not a parameter of 1/r 2 potential.…”