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 factor vanishes are of the form constant Thus they are planes perpendicular to the xy plane How many such planes are there (Values of that differ by are considered to be part of the same plane ) (c) It can be shown that there are l m surfaces on which the factor vanishes What is the shape of these surfaces (d) How many nodal surfaces are there for the real hydrogenlike wave functions

Question: For the real hydrogenlike functions: (a) What is the shape of the n - l - 1 nodal surfaces for which the radial factor is

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?

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