Single Electron Atom Wave Functions
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Schrödinger Equation
The Schrödinger equation describing an electron in a central
field is of the form
In the scaled coordinates that we are using,
and ,
where
is the nuclear charge. The Schrödinger equation for an attractive
Coulomb potential, ,
is
The standard addon package Calculus`VectorAnalysis`
has commands for representing the various vector differential operators
in a number of coordinate systems. First load the package.
Now define a Schrödinger operator,
Set the default coordinate system for the functions from Calculus`VectorAnalysis`
to be spherical polar coordinates:
Now check to see if
is an eigenfunction of the Schrödinger operator.
This of course agrees with the known eigenvalues for the energy
of this system: .
