Spectrum of the non-commutative spherical well

Abstract

We give precise meaning to piecewise constant potentials in non-commutative\nquantum mechanics. In particular we discuss the infinite and finite\nnon-commutative spherical well in two dimensions. Using this, bound-states and\nscattering can be discussed unambiguously. Here we focus on the infinite well\nand solve for the eigenvalues and eigenfunctions. We find that time reversal\nsymmetry is broken by the non-commutativity. We show that in the commutative\nand thermodynamic limits the eigenstates and eigenfunctions of the commutative\nspherical well are recovered and time reversal symmetry is restored.