# The hydrogen atom according to wave mechanics, parts I, II, III, IV, V. (arXiv:1612.05098v2 [physics.gen-ph] UPDATED)

Based on an exposition of the underlying physics and applied mathematics in

arXiv:1603.00899, this paper in five separate parts presents a description of

the properties of the amplitude functions of the hydrogen atom according to

wave mechanics in the coordinate representation in all four systems of

coordinates in which Schroedinger's equations are separable, explicitly I

spherical polar coordinates, II paraboloidal coordinates, III ellipsoidal

coordinates and IV spheroconical coordinates; part V discusses the implications

of these multiple systems in which these atomic orbitals can be directly

calculated. Most published plots of orbitals are inaccurate. In particular,

parts I - IV contain many accurate plots of the surfaces of amplitude functions

in the various systems with a common criterion for the amplitude at which the

surface is constructed. Although the plots are generated from amplitude

functions in the specified systems of coordinates, the plots are translated to

cartesian coordinates that the eye can recognise. The surfaces of the amplitude

functions in ellipsoidal and spheroconical functions are previously unreported,

with the accurate surfaces in spherical polar and paraboloidal coordinates for

a direct comparison.