Tutorials and Unpublished Papers

Quantum Tutorials

Quantum Fundamentals	Atomic Structure
Chemical Bonding	Spectroscopy
Diffraction Phenomena	Group Theory with Mathcad
Quantum Optics	Numerical Solutions for Schrödinger's Equation
Approximate Quantum Mechanical Methods	Miscellaneous

Quantum Fundamentals

An Approach to Quantum Mechanics
Origin of Schrödinger's Equation
Quantum Principles Illuminated with Polarized Light (6/08)
The Relation Between the Coordinate and Momentum Representations (rev. 8/08)
Getting Accustomed to the Superposition Principle (Revised 5/07)
Elements of Dirac Bracket Notation(html)
Elements of Dirac Bracket Notation(pdf)
Illuminating Quantum Mechanical Calculations with Dirac Notation(pdf)
Single Slit Diffraction and the Fourier Transform (6/09)
From Coordinate Space to Momentum Space and Back(6/09)
The Commutation Relation in Position and Momentum Space (6/08)
Simulating the Aharonov-Bohm Effect (9/09)
Matrix Mechanics Using Mathcad (revised 1/08)
The Spatial Double-Slit Experiment
The Double-Slit Experiment with Polarized Light (10/07)
The Double-Slit Experiment with Polarized Light - Mathcad Version (12/07)
The Quantum Eraser (1/08)
Which Way Did It Go? Another Look at the Quantum Eraser (Revised 3/08)
The Temporal Double-Slit Experiment
Comparison of the Spatial and Temporal Double-Slit Experiments
Illustrating Feynman's Sum Over Histories Approach to Quantum Mechanics (2/09)
Evidence for Quantized Gravitational States of the Neutron
Quantized Gravitational States: A Variational Approach
The Quantum Bouncer Doesn't Bounce, Unless... (2/08)
The Importance of Kinetic Energy in the Nanoscale World
Expectation Values and the Variational Principle
Illuminating the Wigner Distribution with Dirac Notation (rev. 10/09)
The Wigner Distribution for the Double Slit Experiment
Basic Quantum Mechanics in Coordinate, Momentum and Phase Space (1/09)
Another Look at the Wigner Function (1/10)
The Wigner Distribution for the Harmonic Oscillator (12/08)
The Wigner Distribution for the Particle in a Box (rev 12/08)
The Wigner Distribution Distinquishes Between a Superposition and a Mixture
The Time-dependent Wigner Distribution for Harmonic Oscillator Transitions
The Momentum Operator in Coordinate Space
Momentum Wavefunctions for the Particle in a Box
A Graphical Illustration of the Uncertainty Principle (revised 1/08)
The Harmonic Oscillator and the Uncertainty Principle (revised 1/08)
Another View of the Harmonic Oscillator and the Uncertainty Principle (2/09)
The Hydrogen Atom and Helium Ion Spatial and Momentum Distribution Functions Illustrate the Uncertainty Principle (1/08)
The Position-Momentum Uncertainty Relation in the Hydrogen Atom (1/08)
The Angular Momentum/Angular Position Uncertainty Relation
A Brief Tutorial on Wavepackets
The Difference Between Fermions and Bosons
Quantum Corrals: Electrons in a Ring (1/09)
Planck's Radiation Equation Fit to Experimental Data
Einstein's Heat Capacity Equation Fit to Experimental Data
Debye's Heat Capacity Equation Fit to Experimental Data
Wave-particle Duality and the Uncertainty Principle
Wave-particle Duality for Matter and Light (7/08)
What Part of the Quantum Theory Don't You Understand? (Power Point Presentation 3/07)
Quantum Potpourri (Power Point Presentation, revised 6/09)
Quantum Dynamics: One Step at a Time (7/08)
Quantum Mechanical Pressure (12/08)
Visualizing the Difference Between a Superposition and a Mixture (7/09)
Analysis of the Stern-Gerlach Experiment Using Matrix Mechanics (8/09)
Bill the Cat and the Superposition Principle (12/09)
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Atomic Structure
The de Broglie-Bohr Model for the Hydrogen Atom (rev. 6/09)
The de Broglie-Bohr Model for the Hydrogen Atom - Version 2 (rev. 6/09)
The de Broglie-Bohr Model for the Hydrogen Atom - Version 3 (rev. 6/09)
Quantum Mechanical Calculations for the One-Dimensional Hydrogen Atom (rev 6/08)
Quantum Mechanical Calculations for the Hydrogen Atom
Atomic Stability
Muonic Hydrogen (5/08)
A Bohr Model for Multi-electron Atoms and Ions
Atomic Variational Calculations: Hydrogen to Boron
Some Calculations on the Lithium Atom Ground State
E. B. Wilson's Calculation on the Lithium Atom Ground State (3/09)
The Importance of the Pauli Principle
Splitting the 2s-2p Degeneracy in the Lithium Atom (1/08)
Hund's Rule
Electron Correlation in Two-electron Systems (3/09)
The Crucial Role of Kinetic Energy in Interpreting Ionization Energies
Quantum Dots Are Artificial Atoms
Calculating the Atomic Radius of Polonium (8/08)
How Many Bibles Can Fit on the Head of a Pin (5/08)
Momentum Wavefunctions and Distributions for the Hydrogen Atom (revised 2/08)
The SCF Method for Two Electrons (revised 03/08)
The SCF Method for Two Electrons Using A Gaussian Wave Function (03/08)
An Interactive SCF Calculation for the Helium Atom (2/08)
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Chemical Bonding
The Covalent Bond and Quantum Mechanics (7/08)
The Covalent Bond in the Hydrogen Molecule
The Covalent Bond Clarified Through the Use of the Virial Theorem
Brief Version of The Covalent Bond Clarified Through the Use of the Virial Theorem
The H₂ Covalent Bond and the Virial Theorem
A Simple Charge Cloud Model for Molecular Hydrogen: Or, Is It a DFT Model? (5/09)
Three Mechanisms for Bond Formation in the Hydrogen Molecule Ion (rev. 1/10)
A Mechanistic Approach to Bond Formation in the Hydrogen Molecule Ion (rev 1/10)
A Lite Version of Ruedenberg's Analysis of the Covalent Bond in Hydrogen Molecule Ion (rev. 3/09)
A One-dimensional Model for the Covalent Bond in Hydrogen Molecule Ion (5/08)
Localized and Delocalized Molecular Orbitals
Two Perspectives on the Bonding in Water
Covalent Bonding in Ammonia from Several Perspectives
A Molecular Orbital Approach to Bonding in Methane (10/09)
A Simple Calculation of the Lattice Energy of LiH
An Even Simpler LiH Lattice Energy Calculation (3/09)
A Critique of the Valence Shell Electron Pair Repulsion Model (Rev. 4/2/07)
A Simple Electrostatic Critique of VSEPR (7/09)
Why Nonbonding Electrons Occupy the Equatorial Position in Trigonal Bipyramidal Geometry (11/07)
A Modified Tangent Spheres Model Analysis of Trigonal Bipyramidal Geometry (11/07)
A Symbolic Huckel MO Calculation Using Mathcad
A Numeric Huckel MO Calculation Using Mathcad
A Numerical Huckel MO Calculation on C₆₀
Chemical Bonding and Electronic Structure of Buckminsterfullerene (7/08)
Quantum Mechanics, Group Theory and C₆₀ (7/08)
A Numerical Huckel Calculation on Anthracene and Phenanthrene (6/07)
A Numerical Huckel Calculation on C₁₀H₈ Isomers (6/08)
Semi-empirical Molecular Orbital Calculation on HF(6/07)
Semi-empirical Molecular Orbital Calculation on XeF₂(6/07)
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Spectroscopy
Rudiments of Atomic Spectroscopy Using Mathcad (rev. 1/08)
A Particle-in-a-Box Model for Color Centers (rev. 4/08)
Cyanine Dyes as Two-State Electronic Systems (11/08)
The Ammonia Inversion and the Maser (Revised 10/08)
The Quantum Jump
Another Look at the Quantum Jump (Revised 3/08)
Quantum Beats (4/08)
The 1s-2s Electronic Transition in the 1D Hydrogen Atom (3/08)
The Quantum Jump in Momentum Space
The Harmonic Oscillator Quantum Jump
Quantum Jumps for an Electron on a Ring (1/09)
Analysis of the Electronic Spectrum of Ti(H₂O)³⁺ (rev 4/08)
Analysis of the Vibrational and Electronic Spectrum of Benzene (6/07)
NMR - Quantum Mechanics of a Three Proton System
The Michelson Interferometer and Fourier Transform Spectroscopy
Modeling the Pi-electrons of Benzene as Particles on a Ring (rev. 1/08)
Calculating the Pi-electron HOMO-LUMO Electronic Transition for Benzene (1/09)
The Vibrational and Electronic States of C₆₀ (4/08)
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Diffraction Phenomena
Using Optical Transforms to Teach Quantum Mechanics
Single-slit Diffraction and the Uncertainty Principle
Single-slit Diffraction and the Uncertainty Principle (Mathcad Version)
Simulating DNA's Diffraction Pattern
Simulating DNA's Diffraction Pattern - Short Version
Is a Two-dimensional Fibonacci Array a Quasilattice?
Calculating Diffraction Patterns
Modeling the C₆₀ Diffraction Pattern
Diffraction Pattern for Hexagonal Point Scatterers
Diffraction Pattern for Hexagonal Finite Point Scatterers
Calculation of the Airy Diffraction Pattern
Diffraction Pattern for Two Concentric Circles
Calculating the Double-Slit Interference Pattern
Density Operator Approach to the Double-Slit Experiment (4-08)
Another Look at the Double-Slit Experiment
A Quantum Mechanical Interpretation of Diffraction
Electron Diffraction at Multiple Slits
The Double-Slit Experiment with C₆₀ Molecules
Crystal Structure and Rotational Symmetry
X-ray Crystallography from a Quantum Mechanical Perspective
X-ray Diffaction
Holography Involves Single Photon Interference
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Group Theory with Mathcad
Dodecahedrane
Xenon Tetrafluoride
Diborane
Cubane
Buckminsterfulerene
BCl₃
Ti(H₂O)₆³⁺
CH₄
P₄
Tetrahedrane (9/09)
PH₃ (9/09)
Cyclopropane (9/09)
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Quantum Optics
Single-Photon Interference - First version
Single-Photon Interference - Second version
Single-Photon Interference - Third version
Single Photon Interference - Mathcad version
Illustrating the Superposition Principle with Single Photon Interference
Two Photon Interference: The Creation of an Entangled Superposition
Two-particle Interference for Bosons and Fermions (5/08)
Another Two Photon Interference Experiment
Two Photon Interference - Matrix Mechanics Approach (rev. 1/10)
Two-electron Interference (7/07)
Quantum Teleportation: A Brief Introduction (6/08)
Greenaberger-Horne-Zeilinger (GHZ) Entanglement and Local Realism (7/08)
Neutron Interferometry with Polarized Spin States (7/08)
Bosonic and Fermionic Photon Behavior at Beam Splitters (8/07)
Pure States, Mixtures and the Density Operator
Polarized Light and the Quantum Superposition (7/08)
Polarized Light and Quantum Mechanics
Matrix Mechanics Approach to Polarized Light
Matrix Mechanics Approach to Polarized Light (Version 2)
Polarized Light and Quantum Mechanics (PDF version)
Spooky Action at a Distance: The EPR Experiment with Photons
God Plays Dice: Quantum Principles Illustrated (Power Point Presentation 2/06)
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Numerical Solutions for Schrödinger's Equation Using Mathcad
Introduction to Numerical Solutions of Schrödinger's Equation Using Mathcad
Particle in an Infinite Potential Well
Particle in a Gravitational Field
Particle in a One-dimensional Egg Carton
Particle in a Finite Potential Well
Particle in a Semi-infinite Potential Well
Particle in a Slanted Potential Well
Numerical Solutions for the Morse Potential
Numerical Solutions for the Harmonic Oscillator
Particle in a Box with an Internal Barrier (rev 6/08)
Another Look at the Particle in a Box with an Internal Barrier (6/08)
Particle in a Box with Multiple Internal Barriers (6/08)
Particle in an Infinite Spherical Potential Well
Numerical Solutions for the Two-Dimensional Harmonic Oscillator
Numerical Solutions for the Three-Dimensional Harmonic Oscillator
Numerical Solutions for the Hydrogen Atom Radial Equation
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Approximate Quantum Mechanical Methods
The Variation Theorem in Dirac Notation (3/09)
Variation Method for a Particle in a Finite Potential Well
Variation Method for a Particle in a Symmetric 1D Potential Well
Variation Method for the Quartic Oscillator
Variation Method for a Particle in a Gravitational Field
Variation Method for a Particle in a Slanted 1D Box
Variation Method for a Particle in a Semi-infinite Potential Well
Variation Method for a Particle in a Box with an Internal Barrier
Variation Method for a Particle in a 1D Ice Cream Cone
Variation Method for a Particle in an Ice Cream Cone
Variation Method for a Particle in a Finite Spherical Potential Well
Variation Method for the Harmonic Oscillator
Trigonometric Trial Wave Function for the Harmonic Potential Well
Trigonometric Trial Wave Function for the 3D Harmonic Potential Well
Gaussian Trial Wave Function for the Hydrogen Atom
Variation Calculation on the 1D Hydrogen Atom Using a Trigonometric Trial Wave Function (3/09)
Variation Calculation on the 1D Hydrogen Atom Using a Gaussian Trial Wave Function (3/09)
Variational Calculation on the Two-dimensional Hydrogen Atom (3/08)
Variational Calculation on Helium Using a Hydrogenic Wave Function (2/08)
Gaussian Trial Wave Function for the Helium Atom (12/07)
Trigonometric Trial Wave Function for the Helium Atom (12/07)
Trigonometric Trial Wave Function for the Hydrogen Atom
Hydrogen Atom Calculation Assuming the Eelctron is a Particle in A Sphere of Radius R (12/07)
Variational Calculations on the Lithium Atom
The Variation Method in Momentum Space
Momentum-Space Variation Method for Particle in a Gravitational Field
Momentum-Space Variation Method for the Quartic Oscillator
Momentum-Space Variation Method for the Abs(x) Potential (2/08)
Variational Method for the Feshbach Potential (6/08)
Numerical Solution for the Feshbach Potential (6/08)
First Order Degenerate Perturbation Theory: The Stark Effect for the Hydrogen Atom (2/08)
Variational Calculation for the Polarizability of the Hydrogen Atom (5/08)
Hybrid Variational Calculation for the 1D Hydrogen Atom with Delta Function Potential (5/08)
Variation Method Using the Wigner Function: Finite Potential Well (12/08)
Variation Method Using the Wigner Function: V(x) = |x| (12/08)
Variation Method Using the Wigner Function: The Quartic Oscillator (12/08)
Variation Method Using the Wigner Function: The Feshbach Potential (12/08)
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Miscellaneous
The Art of Science (revised January 2006)
Commentary on "Probing the Orbital Energy of an Electron in an Atom"
The Use of Models in Introductory Chemistry
Another Great Idea
An Alternative Derivation of Gas Pressure Using the Kinetic Theory
Examining Fourier Synthesis with Dirac Notation (revised 1/09)
Finding Roots of Trancendental Equations
Calculation of the Composition of a Weak Polyprotic Acid Using Mathcad
Solving Linear Equations Using Mathcad
The Global Approach to Thermodynamics: Try It, You'll Like It! (6/08)
Global Thermodynamic Analyses of Heat Engines (11/08)
Using Charles' Law to Determine Absolute Zero (12/08)
The Origin of KE = 3/2 RT (12/08)
Determining the Temperature of the Cosmic Background Radiation

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