A Brief Review of Elementary Quantum Chemistry

C. David Sherrill

Department of Chemistry

University of California, Berkeley

Last Revised on 7 August 2024

Contents

     The Motivation for Quantum Mechanics

          The Ultraviolet Catastrophe

          The Photoelectric Effect

          Quantization of Electronic Angular Momentum

          Wave-Particle Duality

     The Schrodinger Equation

          The Time-Independent Schrodinger Equation

          The Time-Dependent Schrodinger Equation

     Mathematical Background

          Operators

               Operators and Quantum Mechanics

               Basic Properties of Operators

               Linear Operators

               Eigenfunctions and Eigenvalues

               Hermitian Operators

               Unitary Operators

          Commutators in Quantum Mechanics

          Linear Vector Spaces in Quantum Mechanics

     Postulates of Quantum Mechanics

     Some Analytically Soluble Problems

          The Particle in a Box

          The Harmonic Oscillator

          The Rigid Rotor

          The Hydrogen Atom

     Molecular Quantum Mechanics

          The Molecular Hamiltonian

          The Born - Oppenheimer Approximation

          Separation of the Nuclear Hamiltonian

     Solving the Electronic Eigenvalue Problem

          The Nature of Many-Electron Wavefunctions

          Matrix Mechanics

     References

     About this document ...  

---