Some fundamental mathematical properties in atomic and molecular quantum mechanics

The theoretical basis for modeling atomic and molecular systems containing a few particles of electrons and nuclei is the Schrodinger equation and the Born-Oppenheirner separation. The objective of this paper is to review some fundamental mathematical properties for such systems in order to facilitate contemporary interdisciplinary research in quantum computing, quantum control and chemical physics. The following are the main topics addressed in the paper: (1) derivations of the virial theorem and cusp conditions; (2) discussion of H-2(+) (hydrogen molecular ion) orbitals; (3) related examples and illustrations.