Purpose
The purpose of this experiment is to
investigate solutions (Eigenvalues and Eigenfunctions) of the Schroedinger
equation for the Hydrogen atom.
Equipment
and Chemicals
A PC
running Mathematica 3.0, and a printer.
Directions
See the instructor for directions on
how to load and run Mathematica.
Calculations
In Mathematica
a cell is a small segment of the
commands and/or text. You can identify a
cell by the bracket (]) on the right
of the notebook. To execute a command in
a bracket place the cursor behind the command and
type: Shift+Enter.
That is, hold down the Shift key and
press the Enter key.
In this laboratory you will solve the
Hydrogen atom exactly by using Mathematica. The text guides you through the solution of
the problem and gives explanations of the results.
Start at the top of the Notebook which
begins with Vector Calculus. Place the cursor after each successive
command (which are given in bold face) and press Shift+Enter. As you
proceed down the notebook, you will see Mathematica
solve each equation and present algebraic answers and graphics.
Warning: Sometimes Mathematica
takes a few seconds to solve some of the complicated equations. In the upper left hand corner of the notebook
window you will see the work “Running…” whenever Mathematica
is “thinking”. Simply wait a few seconds
and let it complete its work.
At the end of the experiment use the
commands you learn there to plot a wave function for the Hydrogen atom other
than one of those given in the notebook. Print out your graph and answer the following
questions.
Questions
There are no questions for this
experiment, yet!