Evolution from 3-D to 2-D of a confined hydrogen atom dipole dependent properties when compressed by two parallel planes

The confinement of an atom by two parallel planes produces changes in the spectra and dipole-dependent electronic properties when evolving from large-3-D-to narrow-2-D-inter-plane separation. In this work, the behavior of the dipole electronic properties of a hydrogen atom located half the distance between two impenetrable parallel planes is studied as a function of the inter-plane separation using the energies and wave functions reported previously by the author [Physica Scripta 99, 065416 (2024)]. The evolution of the line intensities, transition rates, life times, polarizability, and the mean excitation energy are reported as a function of the inter-plane separation. We find that as the inter-plane separation is reduced, all the electronic properties are affected by the shifting of the electronic spectra towards the short wave-length region (EUV) with a boost of the photo-luminosity intensity, reduction of the static polarizability and life-time of the 2s and 2p states, increase of the mean excitation energy, and transition rates for characteristic plane separations. Our numerical results agree, in the limiting cases, to the analytical solutions for a free atom for large inter-plane separations and to those of a 2-D atom for small inter-plane separation, as well as to available experimental data.