Hydrogen atom in fuzzy spaces - Exact solution

摘要

We investigate consequences of space non-commutativity in quantum mechanics of the hydrogen atom. We introduce rotationally invariant noncommutative space R_0~3 - 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 H of wave functions ψ is formed by properly weighted Hilbert-Schmidt operators in F. We define an analog of the H-atom Hamiltonian in R_0~3 and explicitly determine the bound state energies E_n~λ and the corresponding eigenstates ψ_(njm)~λ.