AbstractWe perform an analytical study on the allowance of forbidden transitions for a hydrogen atom placed near line dipole sources, mimicking light emanating from a one-dimensional metallic nanogap. It is shown that the rapid variation of the electric field vector, inevitable in the near zone, completely breaks the selection rule of Δl=±1. While the forbidden transitions between spherically symmetric S states, such as 2S to 1S or 3S to 1S (Δl=0), are rather robust against selection rule breakage, Δl=±2 transitions such as between 3D and 1S or 3D and 2S states are very vulnerable to the spatial variation of the perturbing electric field. Transitions between 2S and 3D states are enhanced by many orders of magnitude, aided by the quadratic nature of both the perturbing Hamiltonian and D wavefunctions. The forbidden dipole moment, which approaches one Bohr radius times the electric charge in the vicinity of the gap, can be written in a simple closed form owing to the one-dimensional nature of our gap. With large enough effective volume together with the symmetric nature of the excited state wavefunctions, our work paves way towards atomic physics application of infinitely long nanogaps.
Is Dirichlet the physical boundary condition for the one-dimensional hydrogen atom?