The Mathematica electronic notebooks developed for Quantum Mechanics I-II (Physics 309-310) are available below along with a description of how to load them onto your computer. All of the notebooks have been tested on a Macintosh and a linux machine. If you have any problems send me email at ggilfoyl@richmond.edu

The Mathematica Notebook files contain ASCII text, and can be transferred by email, ftp, or other text-file transfer utility. If you click on the file with a web browser you will see all the formatting instructions in addition to the actual contents of the notebook. You should save the file as it appears with a name ending with ".nb" to allow Mathematica to recognize it as a Notebook. The file can then be read or edited using a copy of Mathematica or MathReader. If you received a file through another route (e.g., email) copy/paste to save everything in the file from the line containing (*^ down to the line containing ^*) into a plain text file.

Note: Some of the files are Mathematica movies. These files are often too cumbersome to download with a browser so I have also included a file with only the commands needed to generate the movie.

• Introduction.nb Notebook that introduces the Mathematica computing environment and shows how to make a few calculations and plots.

• TravelingWaves.nb Laboratory that demonstrates the functional form required for any wave that propagates through space.

• CentralPotentials.nb Laboratory that illustrates some of the classical features of radial potential energy functions.

• Superposition.nb Laboratory that demonstrates how individual waves (eigenfunctions) can add up to form a wave packet that even has 'sharp' edges.

• Orthonormality.nb This lab illustrates visually the nature of orthogonal functions and studies the uncertainty principle.

• Uncertainty.nb The 'chopped beam' problem is analyzed and an uncertainty principle is derived.

• Lists.nb Laboratory that demonstrates how to make a list in Mathematica and plot it.

• FourierSeriesMovieCmnd3.nb This file contains the commands used to create the movie for an initial square in a box. It is small in size so it can be downloaded quickly, but you then have to execute the commands to generate the movie.

• GaussianMovieCmnd.nb This file contains the commands used to create a movie of a Gaussian wave packet composed of free particle eigenfunctions. It is small in size so it can be downloaded quickly, but you then have to execute the commands to generate the movie.

• TimeDevelopment.nb Laboratory that investigates the time development of a Gaussian wave packet composed of free particle wave functions.

• COspectrum.nb Data from electron-CO collisions is analyzed to test the validity of modelling the carbom-oxygen bond in CO as a harmonic oscillator.

• ClassicalFusion.nb Laboratory that investigates the paradox of solar energy production. Used to introduce the need for quantum mechanical tunneling to adequately explain the Sun's energy production.

• 1DSolid.nb Laboratory that 'builds' a one-dimensional metal starting from a single rectangular barrier. We use the transfer matrix method to propagate waves through the barriers.

• AlphaDecay.nb Laboratory that studies the systematics of nuclear alpha decay. The calculation of the transmission coefficient uses a transfer matrix approach that takes advantage of the matrix multiplication capabilities of Mathematica. See A new teaching approach to quantum mechanical tunneling (Computer Physics Communications 121–122 (1999) 573–577) and Alpha Decay Laboratory in Mathematica in Education and Research, 4, No. 1, p. 19, Winter, 1995.

• AlphaDecay2.nb Laboratory that studies the systematics of nuclear alpha decay. The calculation of the transmission coefficient uses the expression developed in Gasiorowiscz and then applies the method of Gamow, Condon, and Gurney to estimate the lifetimes.

• SecondOrderDE.nb Laboratory that uses a numerical integration of the harmonic oscillator differential equation to develop these computational methods.

• DeuteronState.nb Laboratory that investigates the nature of the nuclear force to understand why the deuteron has a single bound state. Uses a finite difference method to numerically integrate the Schroedinger equation and determine the bound-state energy levels.

• SquareWell.nb Laboratory that uses a numerical integration of the Schroedinger equation to find the bounds states of a particle in a finite square well.

• VisualizingPls.nb Introduction to the Legendre polynomials and shows how they depend on the angular momentum quantum number l.

• COrotatorLab.nb The rotation-vibration spectrum of the carbon monoxide (CO) molecule is analyzed. A plot of the data is included here and a listing of the peak energies is here.

• ScatteringWaveFunc.nb Investigate the effects of a realistic nucleus-nucleus force on the radial part of the free particle wave in three dimensions.

• FitScattering.nb Extract the angular momentum composition of ⁴He -¹²C elastic scattering to distinguish between two competing models of the structure of ¹⁶O.

• Hydrogen Lab Experimental laboratory to measure the wavelengths of the hydrogen emission lines, determine their energies, and compare the measurements with the prediction of the Schroedinger equation with the Coulomb potential.

• HydrogenOrbitals.nb Laboratory to visualize the probability density of the electron in the hydrogen atom using a density plot in Mathematica.

• HydrogenOrbitalsV2.nb Delve deeper into the nature of the hydrogen orbitals and compare our understanding with some old pictures from our earliest childhood. This lab uses a Wolfram demonstration that is here.

• HydrogenMonteCarlo.nb Laboratory to visualize the probability density of the electron in the hydrogen atom. Uses a Monte Carlo technique to produce a scatter plot weighted by the probability density and uses Mathematica's 'four-dimensional' plotting capabilities.

• LScoupling.nb Laboratory to investigate the nature of the spin-orbit coupling in the hydrogen atom and introduce some of Mathematica's tools for finding eigenvalues and eigenfunctions of matrices.

• FineStructure.nb Laboratory to study the hydrogen atom fine structure that includes the spin-orbit and relativistic corrections to the Coulomb potential in the Schroedinger equation. Uses Mathematica's tools for finding eigenvalues and eigenfunctions of matrices.

• HydrogenZeeman.nb Laboratory to study the Zeeman effect in the hydrogen atom. The theoretical calculation includes the spin-orbit and relativistic corrections to the Coulomb potential in the Schroedinger equation and the influence of an external magnetic field. A calculation is performed of the magnetic field dependence of the energy states and a comparison made with the data of Lamb and Retherford.

• Polarization.nb Laboratory to demonstrate photon polarization and investigate its mathematical nature. The requirements for circular polarization are developed and mathematical movies made to illustrate the concepts.