On the repulsive nature of the Dirichlet boundaries in the confined atom problem

An atom in a box with penetrable or impenetrable potential walls is shown analytically to move under the influence of the repulsive forces from the boundaries of the cavity when all the atom-medium interactions are described by the Dirichlet boundary conditions or effective one-particle `box' potentials. Simple geometrical methods allow one to find the energetically optimal position of the atom in the cavity. For instance, the ground state energy of the hydrogen atom is proved to be minimal when the nucleus is situated at the centre of the cube or sphere. Some applications for molecules are also mentioned.