Noncommutative quantum mechanics - art. no. 067901

A general noncommutative quantum mechanical system in a central potential V = V(r) in two dimensions is considered. The spectrum is bounded from below and, for large values of the anticommutative parameter theta, we find an ex plicit expression for the eigenvalues. In fact, any quantum mechanical syst em with these characteristics is equivalent to a commutative one in such a way that the interaction V(r) is replaced by V = V((H) over cap (HO), (L) o ver cap (z)), where (H) over cap (HO) is the Hamiltonian of the two-dimensi onal harmonic oscillator and (L) over cap (z) is the z component of the ang ular momentum. For other finite values of theta the model can be solved by using perturbation theory.