Confinement of hydrogen atom with Dirac equation

摘要

The problem of a particle confined in a spherical cavity is studied with the Dirac equation. A hard confinement is obtained by forcing the large component to vanish at the cavity radius. It is shown that the small component cannot vanish simultaneously at this radius. In the case of a confined hydrogen atom, the energies are given by an implicit equation. For some values of the radius, explicit analytical expressions of the energy exist like in the nonrelativistic case. Very accurate energies and wave functions are obtained with the Lagrange-mesh method with few mesh points. To this end, two differently regularized Lagrange-Jacobi bases associated with the same mesh are used for the large and small components. The importance of relativistic effects is discussed for hydrogenlike ions. The validity of this definition of hard confinement is discussed with a soft-confinement model studied with the R-matrix method.