Shell-confined hydrogen atom

Calculations of electronic energy and static dipole polarizability are reported for the hydrogen atom in the ns states (n = 1-6) confined between two impenetrable concentric spheres of inner and outer radii placed at the locations of the radial nodes corresponding to the free hydrogen ns (n = 2-7) orbitals. Interesting new conditions of degeneracy arising due to the shell confinement are discussed. Shell-confined states of unusually high polarizability are predicted for hydrogen atom as the inner sphere radius is shifted towards the outer nodal points of the free atom corresponding to the higher principal quantum numbers.