The Dispersion by Hydrogen-Like Atoms in Undulatory Mechanics.

1. In view of the recent experimental determination of the dispersion by atomic hydrogen' it seems interesting to apply the theory of dispersion developed by Schrodinger2 to this case. In this paper we restrict ourselves to an approximation in which terms of the order of relativistic correction are neglected. For this purpose it is simpler to obtain our wave equation by the operational method of Schrodinger3 and Eckart,4 as extended by Epstein," for in this way we immediately obtain an equation free of relativistic terms. 2. We assume the incident light to be a plane polarized wave of frequency v propagated along the Y axis, with the electric vector along Z, the nucleus being situated at the origin. The field of the wave and of the nucleus can be represented by a vector potential A and a scalar potential 4. We take Ax = Ay = 0, Az = -c2F sin w(t y/c)/w, and 4, = Kelr, where w = 27rP, Ke the charge of the nucleus, c the velocity of light and F a constant, all quantities being in electrostatic units. The corresp`onding Hamiltonian function is