The Lenz vector in the confined hydrogen atom problem

A general criterion for the degeneracy of states of the hydrogen atom placed in a spherical impenetrable box of radius R is formulated on the basis of the Lenz vector formalism. The reasons for the elimination of the Coulomb degeneracy typical of the conventional hydrogen atom problem and for the non-conservation of the Lenz vector are discussed. The explanation of the simultaneous degeneracy of some energy levels (e.g. 2s and 3d, 3s and 4d, etc. at R=2 au) is given.