Spectrum of the non-commutative spherical well

Abstract

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