The magnetic two-centre problem: some rigorous properties

Abstract

We study the quantum mechanical magnetic two-centre problem, i.e., quantum states of an electron within the Coulomb field of two fixed nuclear centres and a homogeneous magnetic field. From the corresponding nonrelativistic Schrödinger equation various characteristic properties are derived. These include the ordering of energy levels and the monotonicity of electronic energies as a function of the nuclear separation if the internuclear axis is parallel to the direction of the B field. For such situations we also obtain lower bounds on the equilibrium separation between the nuclei and establish decay properties of bound state wavefunctions. Moreover, the molecular virial theorem is generalized to encompass the contributions from the magnetic field.