James F Harrison

Emeritus Professor of Chemistry

Chemistry Department

Michigan State University

East Lansing Michigan 48824





Courses taught 1968-2103


Publications 1967-2017



Over the years I have taught many courses and the notes for a few of the topics discussed are collected below.


This first grouping includes some basic classical physics the understanding of which is vital for success in Advanced Physical Chemistry.




            Electrostatic potential & electric field due to a collection of point charges

            Potential energy of a collection of N point charges

            Potential energy of N point charges in an external potential

            Multipole moments of a charge distribution

            Multipole expansion of a charge distribution

            Interaction energy between two disjoint charge distributions



Angular Momentum


            Orbital angular momentum operators

            Angular momentum in a central field


            Eigenvalues and Eigenfunctions of Orbital Angular Momentum

            Operator Derivation of Eigenvalue and Eigenfunctions

            A spin ½ particle in a Central Potential

            Coupling of Angular Momenta

            Wigner or Clebsch-Gordon Coeffficients



Perturbation theory

            Non-degenerate theory

                                    Non-degenerate examples

                                                Harmonic oscillator with a cubic perturbation

                                                Harmonic oscillator in a constant electric field

                                                Moller-Plesset second order theory

            Degenerate  theory                             



Hydrogen-like atoms/ions


            Schrodinger equation

                        Center of Mass Separation

                        Energy and Structure of Wavefunctions

                        Radial Distribution Functions

                        Average values of rn

                        Comparison with experiment

            One-electron Atoms in an Electric Field

                        Ground state (Stark Effect, dipole & quadrupole polarizabilities)

                        Excited State (Stark Effect)

            Spin-orbit Interaction

                        Form of the Hamiltonian

                        Angular and Radial Wave-functions

                        PerturbationTreatment (numerical results)

            One-electron atoms in a magnetic field

            More Relativistic Effects

                        Dirac equation for a one-electron atom

                        Pauli Hamiltonian and the Mass Velocity, Spin Orbit & Darwin Terms

                        First-order perturbation results using Pauli Hamiltonian

                        Exact Energy Eigenvalues of Dirac equation


                        Hydrogen wavefunctions (1s-6h)




Hartree-Fock Theory



            General Equations

            Unrestricted open-shell


            Restricted open-shell

            Physical interpretation

            Relationship between Hartree-Fock eigenvalues and the Energy

            Matrix Hartree-Fock equations

            Spin Contamination in UHF



Density Matrices, Natural Orbitals & Electron Density



                        One and Two Particle Density Matrices-Definitions

                        One and Two Particle Density Matrices for Hartree-Fock wavefunctions

                        Electron Density and one Particle Density Matrix

                        Natural Orbitals and One Particle Density Matrix

                        Natural Orbitals for Heitler-London H2


Slater Determinants


                        Slater Determinants and Antisymmeteriizing Operator

                        Matrix Elements Between Slater Determinants (Slater-Condon Rules)


Spin and Many Electron Systems


                        One Electron Spin Operators

                        Many Electron Spin Operators

                        Two Electron Spin Eigenfunctions

                        Many Electron Spin Eigenfunctions



He and Two Electron Atoms



                        Orbital Models

                        Hartree-Fock equations

                        Correlation Energy

                        Hylleraas Equation