Energy levels of the hydrogen atom in a cylindrical cavity

Electronic states of the cylindrically confined hydrogen atom are studied numerically by the finite difference (FD) approach. Energies of the low-lying states of the system are estimated vs. the radius R and length Z of the cylinder, as well as the position of the nucleus at the axis. Under the isotropic stretch of the cylinder with the constant ratio R = Z/2, the energy level picture reminds us that in the spherically confined atom: the energies of all states regularly grow up when decreasing the size of the cavity, and the states with the same principal n, but higher values of the angular l quantum number correspond to lower energies almost everywhere. Anisotropic stretch of the cylinder from prolate to the oblate one with constant volume causes numerous level intersections and avoided crossings, with the levels ordered as 1σ, 2π, 3δ, 2σ,…, in the prolate limit case, and as 1σ, 2π, 2σ, 3δ, 3π, 3σ,…, in the oblate limit case. The results of numerical calculations are in excellent agreement with qualitative consideration of the one-electron system in the impenetrable cavity by using both variational and perturbative approaches. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006