Suppressing the spurious states of the centre of mass

Abstract

Following Dirac's ideas concerning the quantization of constrained systems, we suggest to replace the free centre of mass Hamiltonian H_{CM} by another operator which commutes with all the elements of the algebra generated via the commutation relations by H_{CM} and the constraints which fix the centre of mass position. We show that the new Hamiltonian is a multiple of the identity operator and, as a result, its unique effect is to raise the internal energy levels by a constant amount.