On a quantum mechanical example connected with compatability of observables

Two quantum mechanical observables with purely discrete spectra (energy operator and square of momentum) of a quasiparticle moving in a crystal medium are considered. These observables are defined as the unique self-adjoint extensions of certain differential expressions obtained from physical condiderations and represented mathematically by commuting symmetric operators. From a general theorem (previously proved by one of the authors) on commutativity of such self-adjoint extensions follows that compatibility of the two observables in von Neumann's sense depends on the geometric form of the crystal surface. (Auth.)