Hydrogen atom in fuzzy spaces - Exact solution

Abstract

We investigate consequences of space non-commutativity in quantum mechanics of the hydrogen atom. We introduce rotationally invariant noncommutative space R̂03 - an analog of the hydrogen atom (H-atom) configuration space which is generated by noncommutative coordinates realized as operators in an auxiliary (Fock) space F The Hilbert space Ĥ of wave functions ψ is formed by properly weighted Hilbert-Schmidt operators in F. We define an analog of the H-atom Hamiltonian in R̂03 and explicitly determine the bound state energies Enλ and the corresponding eigenstates ψnjmλ.