For the real hydrogenlike functions:
(a) What is the shape of the n - l - 1 nodal surfaces for which the radial factor is zero?
(b) The nodal surfaces for which the ϕ factor vanishes are of the form ϕ = constant. Thus they are planes perpendicular to the xy plane. How many such planes are there? (Values of ϕ that differ by π are considered to be part of the same plane.)
(c) It can be shown that there are l - m surfaces on which the θ factor vanishes. What is the shape of these surfaces?
(d) How many nodal surfaces are there for the real hydrogenlike wave functions?