University Physics Notes: Quantum Mechanics – Features of Solutions of the Schrodinger Equation for the Hydrogen Atom
The general solution of the Schrodinger equation corresponding to
a principal quantum number is a polynomial in
of
degree
with
circles
of zero electron density multiplied by a polynomial in
(
or
or
both) of degree
with
radial
lines of zero electron density, which occur in oppositely directed
pairs, illustrated on the diagram below, multiplied by a complex
exponential in
of
magnitude 1.