Quantum Tutorials

Quantum Fundamentals
Atomic Structure
Chemical Bonding
Spectroscopy
Diffraction Phenomena
Group Theory with Mathcad
Quantum Optics
Single-particle Interference
Two-particle Interference
Quantum Teleportation
Quantum Correlations & Bell's Theorem
Quantum Computation
Numerical Solutions for
Schrödinger's Equation
Approximate Quantum
Mechanical Methods

Miscellaneous

    Quantum Fundamentals

  1. An Approach to Quantum Mechanics

  2. Quantum Mechanics and the Fourier Transform (10/10)

  3. Origin of Schrödinger's Equation

  4. Basic Quantum Mechanics in Coordinate, Momentum and Phase Space (1/09)

  5. The Repackaging of Quantum Weirdness (4/10)

  6. Quantum Principles Illuminated with Polarized Light (6/08)

  7. The Relation Between the Coordinate and Momentum Representations (rev. 8/08)

  8. A Very Brief Demonstration of the Relation Between the Coordinate and Momentum Representations (rev. 8/10)

  9. Getting Accustomed to the Superposition Principle (Revised 5/07)

  10. The Dirac Delta Function Illustrated (5/12)

  11. Elements of Dirac Bracket Notation(pdf)

  12. Illuminating Quantum Mechanical Calculations with Dirac Notation(pdf)

  13. The Creation and Annihilation Operators (revised 5/12)

  14. Single Slit Diffraction and the Fourier Transform (6/09)

  15. From Coordinate Space to Momentum Space and Back(6/09)

  16. The Commutation Relation in Position and Momentum Space (6/08)

  17. Simulating the Aharonov-Bohm Effect (9/09)

  18. Basic Matrix Mechanics (4/17)

  19. Rudimentary Matrix Mechanics (rev. 12/15)

  20. Matrix Mechanics Using Mathcad (revised 1/12)

  21. Aspects of Dirac's Relativistic Matrix Mechanics (8/14)

  22. The Spatial Double-Slit Experiment

  23. The Double-Slit Experiment with Polarized Light (10/07)

  24. The Consequences of Path Information in a Mach-Zehnder Interferometer (2/17)

  25. Another look at the Consequences of Path Information in a Mach-Zehnder Interferometer (5/18)

  26. The Double-Slit Experiment with Polarized Light - Mathcad Version (12/07)

  27. The Quantum Eraser (rev. 12/12)

  28. Which Way Did It Go? Another Look at the Quantum Eraser (Revised 12/12)

  29. Which Path Information and the Quantum Eraser (9/16)

  30. Which Path Information and the Quantum Eraser - Brief Version (3/17)

  31. Triple Slit Diffraction with an Eraser (5/18)

  32. Which-way Markers and Pre-selection in the Double-slit Experiment (4/16)

  33. A Stern-Gerlach Quantumn Eraser (rev. 3/17)

  34. Impact of Which-way Information in the Mach-Zehnder Interferometer (7/10)

  35. Quantum Theory, Wave-Particle Duality and the Mach-Zehnder Interferometer (6/18)

  36. The Temporal Double-Slit Experiment

  37. Comparison of the Spatial and Temporal Double-Slit Experiments

  38. An Analysis of Three-Path Interference (rev. 5/16)

  39. Illustrating Feynman's Sum Over Histories Approach to Quantum Mechanics (revised 9/14)

  40. The Paradox of Recombined Beams (9/14)

  41. Evidence for Quantized Gravitational States of the Neutron

  42. Quantized Gravitational States: A Variational Approach

  43. The Quantum Bouncer Doesn't Bounce, Unless... (2/08)

  44. The Importance of Kinetic Energy in the Nanoscale World

  45. Expectation Values and the Variational Principle

  46. The Wigner Function Illuminated with Dirac Notation (rev. 10/10)

  47. The Wigner Distribution for the Single Slit Experiment (3/13)

  48. The Wigner Distribution for the Double Slit Experiment (rev. 9/12)

  49. The Wigner Distribution for the Triple Slit Experiment (9/12)

  50. The Wigner Distribution for the Quadruple Slit Experiment (5/16)

  51. Quantum Mechanical Tunneling in Coordinate, Momentum and Phase Space (5/10)

  52. Another Look at the Wigner Function (1/10)

  53. The Wigner Distribution for the Harmonic Oscillator (8/15)

  54. The Wigner Distribution for the Particle in a Box (rev 12/08)

  55. The Wigner Distribution for the Particle in a Box - Another Look (3/17)

  56. The Wigner Distribution Distinquishes Between a Superposition and a Mixture

  57. The Time-dependent Wigner Distribution for Harmonic Oscillator Transitions (revised 1/11)

  58. The Momentum Operator in Coordinate Space

  59. Momentum Wavefunctions for the Particle in a Box (rev. 6/13)

  60. A Graphical Illustration of the Uncertainty Principle (revised 10/10)

  61. The Quantum Oscillator (8/12)

  62. The Harmonic Oscillator and the Uncertainty Principle (revised 5/10)

  63. Another View of the Harmonic Oscillator and the Uncertainty Principle (Rev. 9/14)

  64. The Hydrogen Atom and Helium Ion Spatial and Momentum Distribution Functions Illustrate the Uncertainty Principle (1/08)

  65. The Position-Momentum Uncertainty Relation in the Hydrogen Atom (1/08)

  66. The Angular Momentum/Angular Position Uncertainty Relation

  67. A Brief Tutorial on Wavepackets

  68. The Difference Between Fermions and Bosons

  69. Quantum Corrals: Electrons in a Ring (1/09)

  70. Planck's Radiation Equation Fit to Experimental Data

  71. Planck's Radiation Equation Fit to Experimental Data - Another Algorithm (9/10)

  72. Einstein's Heat Capacity Equation Fit to Experimental Data

  73. Einstein's Heat Capacity Equation Fit to Experimental Data - Another Algorithm (9/10)

  74. Debye's Heat Capacity Equation Fit to Experimental Data

  75. Debye's Heat Capacity Equation Fit to Experimental Data - Another Algorithm (9/10)

  76. Wave-particle Duality and the Uncertainty Principle (revised 5/13)

  77. Wave-particle Duality for Matter and Light (7/08)

  78. What Part of the Quantum Theory Don't You Understand? (Power Point Presentation 3/07)

  79. Quantum Potpourri (Power Point Presentation, revised 6/09)

  80. Quantum Dynamics: One Step at a Time (7/08)

  81. Quantum Mechanical Pressure (12/08)

  82. Visualizing the Difference Between a Superposition and a Mixture (7/09)

  83. Analysis of the Stern-Gerlach Experiment Using Matrix Mechanics (8/09)

  84. Related Analysis of the Stern-Gerlach Experiment (12/10)

  85. Bill the Cat and the Superposition Principle (12/09)

  86. Schroedinger's Dog (10/17)

  87. The Bloch Sphere (7/10)

  88. Density Matrix, Bloch Vector and Entropy (rev. 1/14)

  89. State Vectors and State Operators: Superpositions, Mixed States and Entanglement (rev. 8/14)

  90. The Gram-Schmidt Proceedure (3/14)

    Return to top of page.

    Atomic Structure

  91. The de Broglie-Bohr Model for the Hydrogen Atom (rev. 6/09)

  92. The de Broglie-Bohr Model for the Hydrogen Atom - Version 2 (rev. 6/09)

  93. The de Broglie-Bohr Model for the Hydrogen Atom - Version 3 (rev. 6/09)

  94. The de Broglie-Bohr Model for a Hydrogen Atom Held Together by a Gravitational Interaction (2/11)

  95. The de Broglie-Bohr Model for Positronium (10/13)

  96. The Bohr Model for the Earth-Sun System (9/12)

  97. Extracting Atomic & Molecular Parameters From the deBroglie-Bohr Model of the Atom (revised 11/17)

  98. Electronic Structure and the Superposition Principle (9/11)

  99. Atomic Spectroscopy and the Correspondence Principle (9/10)

  100. Hydrogen-Like Calculations with Variable Lepton Mass (6/16)

  101. Quantum Mechanical Calculations for the One-Dimensional Hydrogen Atom (rev 6/08)

  102. Quantum Mechanical Calculations for the Hydrogen Atom

  103. Atomic Stability

  104. Atomic Stability - Mathcad Version

  105. Critique of the Centrifugal Effect in the Hydrogen Atom (rev. 5/16)

  106. A Shorter Critique of the Centrifugal Effect in the Hydrogen Atom (5/16)

  107. Exploring the Role of Lepton Mass in the Hydrogen Atom (revised 7/14)

  108. The Effect of Lepton Mass on the Energy and Bond Length of the Hydrogen Molecule Ion (3/113)

  109. The Hydrogen Atom with Finite Sized Nucleus (8/10)

  110. The Hyperfine Interaction in the Hydrogen Atom (rev. 11/12)

  111. Positronium Annihilation (rev. 1/16)

  112. Positronium Annihilation: Another View (8/16)

  113. The Hyperfine Interaction in the Deutrium Atom (rev. 7/14)

  114. A Tensor Algebra Approach to Spin-Orbit Coupling (9/12)

  115. A Bohr Model for Multi-electron Atoms and Ions

  116. Atomic Variational Calculations: Hydrogen to Boron

  117. Some Calculations on the Lithium Atom Ground State

  118. E. B. Wilson's Calculation on the Lithium Atom Ground State (3/09)

  119. The Importance of the Pauli Principle (3/10)

  120. Splitting the 2s-2p Degeneracy in the Lithium Atom (1/08)

  121. Addition of Spin Angular Momentum: A Tensor Algebra Approach (12/12)

  122. Hund's Rule

  123. Electron Correlation in Two-electron Systems (3/09)

  124. The Crucial Role of Kinetic Energy in Interpreting Ionization Energies

  125. Quantum Dots Are Artificial Atoms

  126. Calculating the Atomic Radius of Polonium (8/08)

  127. Calculating the Atomic Radius of Gold (9/12)

  128. How Many Bibles Can Fit on the Head of a Pin (5/08)

  129. Momentum Wavefunctions and Distributions for the Hydrogen Atom (revised 2/08)

  130. The SCF Method for Two Electrons (revised 03/08)

  131. Outline of the SCF Method for Two Electrons (09/12)

  132. The SCF Method for Two Electrons Using A Gaussian Wave Function (03/08)

  133. An Interactive SCF Calculation for the Helium Atom (2/08)

  134. Quantum Calculations on the Hydrogen Atom in Coordinate, Momentum and Phase Space (3/16)

  135. The Wigner Distribution for the 1s State of the 1D Hydrogen Atom (5/16)

  136. The Wigner Distribution for the 2s State of the 1D Hydrogen Atom (6/12)

  137. The Wigner Distribution for the 2p State of the 1D Hydrogen Atom (5/16)

  138. The Wigner Distribution for the 3s State of the 1D Hydrogen Atom (6/12)

  139. The Wigner Distribution for the 3p State of the 1D Hydrogen Atom (5/16)

  140. The Wigner Distribution for the 4s State of the 1D Hydrogen Atom (9/12)

  141. One-dimensional H-atom with Delta Function Potential (12/12)

  142. The Atomic Structure Factor in Coordinate and Momentum Space (6/13)

    Return to top of page.

    Chemical Bonding

  143. The Covalent Bond and Quantum Mechanics (7/08)

  144. The Covalent Bond in the Hydrogen Molecule

  145. The Covalent Bond Clarified Through the Use of the Virial Theorem

  146. Brief Version of The Covalent Bond Clarified Through the Use of the Virial Theorem

  147. The H2 Covalent Bond and the Virial Theorem

  148. The Covalent Bond According to Slater and Ruedenberg

  149. Slater's Analysis of the Covalent Bond using the Virial Theorem(rev. 4/17)

  150. Two Analyses of the Covalent Bond using the Virial Theorem(12/17)

  151. A Simple Charge Cloud Model for Molecular Hydrogen: Or, Is It a DFT Model? (5/09)

  152. Three Mechanisms for Bond Formation in the Hydrogen Molecule Ion (rev. 2/12)

  153. A Mechanistic Approach to Bond Formation in the Hydrogen Molecule Ion (rev 3/11)

  154. A Lite Version of Ruedenberg's Analysis of the Covalent Bond in Hydrogen Molecule Ion (rev. 3/10)

  155. Molecular Orbital Analysis for the Hydrogen Molecule Ion Bond (3/13)

  156. A One-dimensional Model for the Covalent Bond in Hydrogen Molecule Ion (5/08)

  157. Localized and Delocalized Molecular Orbitals

  158. Two Perspectives on the Bonding in Water

  159. Covalent Bonding in Ammonia from Several Perspectives

  160. A Molecular Orbital Approach to Bonding in Methane (10/09)

  161. A Simple Calculation of the Lattice Energy of LiH (rev 12/10)

  162. An Even Simpler LiH Lattice Energy Calculation (3/09)

  163. Charge Cloud Models for Some Simple Atomic, Molecular and Solid Systems (rev. 8/17)

  164. A Critique of the Valence Shell Electron Pair Repulsion Model (Rev. 4/2/07)

  165. A Simple Electrostatic Critique of VSEPR (7/09)

  166. Another Critique of VSEPR (7/17)

  167. Why Nonbonding Electrons Occupy the Equatorial Position in Trigonal Bipyramidal Geometry (11/07)

  168. A Modified Tangent Spheres Model Analysis of Trigonal Bipyramidal Geometry (11/07)

  169. A Symbolic Huckel MO Calculation Using Mathcad

  170. A Numeric Huckel MO Calculation Using Mathcad

  171. A Numerical Huckel MO Calculation on C60

  172. Chemical Bonding and Electronic Structure of Buckminsterfullerene (7/08)

  173. Quantum Mechanics, Group Theory and C60 (7/08)

  174. A Numerical Huckel Calculation on Anthracene and Phenanthrene (6/07)

  175. A Numerical Huckel Calculation on C10H8 Isomers (6/08)

  176. Semi-empirical Molecular Orbital Calculation on HF(6/07)

  177. Semi-empirical Molecular Orbital Calculation on XeF2(6/07)

  178. Posch-Teller Potential Model for Metals (9/12)

    Return to top of page.

    Spectroscopy

  179. Rudiments of Atomic Spectroscopy Using Mathcad (rev. 1/08)

  180. A Particle-in-a-Box Model for Color Centers (rev. 4/08)

  181. Cyanine Dyes as Two-State Electronic Systems (11/08)

  182. The Ammonia Inversion and the Maser (Revised 10/08)

  183. A Symmetric Double Well Potential Illustrating Tunneling (2/13)

  184. Analyses of the Pure Rotational Spectrum of HCl (8/10)

  185. A Rudimentary Analysis of the Vibrational-Rotational HCl Spectrum (8/10)

  186. Visualizing the Formally Forbidden Overtone Vibrational Transitions in HCl (2/10)

  187. The Quantum Jump

  188. Another Look at the Quantum Jump (Revised 3/08)

  189. Quantum Beats (4/08)

  190. The 1s-2s Electronic Transition in the 1D Hydrogen Atom (3/08)

  191. The Quantum Jump in Momentum Space (rev. 6/13)

  192. The Harmonic Oscillator Quantum Jump

  193. Coherent States of the Harmonic Oscillator (8/12)

  194. Quantum Jumps for an Electron on a Ring (1/09)

  195. Analysis of the Electronic Spectrum of Ti(H2O)3+ (rev 4/08)

  196. Analysis of the Vibrational and Electronic Spectrum of Benzene (6/07)

  197. NMR - Quantum Mechanics of a Three Proton System

  198. AB Proton NMR Using Tensor Algebra (4/10)

  199. Calculating the AB Proton NMR Using Tensor Algebra (11/10)

  200. AB Proton NMR Analysis for 2,3-dibromothiophene (12/10)

  201. ABC Proton NMR Using Tensor Algebra (11/10)

  202. AB2 Proton NMR Using Tensor Algebra (2/13)

  203. AB3 Proton NMR Using Tensor Algebra (2/13)

  204. HD-Like NMR Spectrum Calculated Using Tensor Algebra (8/11)

  205. The Michelson Interferometer and Fourier Transform Spectroscopy

  206. A Sum Over Histories Approach to Fourier Transform Infrared Spectroscopy (10/13)

  207. Modeling the Pi-electrons of Benzene as Particles on a Ring (rev. 1/08)

  208. Modeling the Pi-electrons of Benzene as Particles on a Ring - Version 2 (12/15)

  209. Calculating the Pi-electron HOMO-LUMO Electronic Transition for Benzene (1/09)

  210. Modeling the Pi-electrons of Benzene as Particles in a Ring (8/14)

  211. Modeling the Pi-electrons of Corannulene as Particles in a Ring (8/14)

  212. The Vibrational and Electronic States of C60 (4/08)

    Return to top of page.

    Diffraction Phenomena

  213. Using Optical Transforms to Teach Quantum Mechanics

  214. Single-slit Diffraction and the Uncertainty Principle

  215. Single-slit Diffraction and the Uncertainty Principle (Mathcad Version)

  216. Simulating DNA's Diffraction Pattern

  217. Simulating DNA's Diffraction Pattern with a More Realistic Model

  218. Simulating DNA's Diffraction Pattern - Short Version

  219. A Model Graphene Diffraction Pattern (6/13)

  220. Is a Two-dimensional Fibonacci Array a Quasilattice?

  221. Calculating Diffraction Patterns

  222. Modeling the C60 Diffraction Pattern

  223. Diffraction Pattern for Pentagonal Point Scatterers (5/13)

  224. Diffraction Pattern for Pentagonal Finite Point Scatterers (5/13)

  225. Pentagram Diffraction Pattern (5/13)

  226. Model Diffraction Pattern for Napthalene (5/13)

  227. Calculating the Airy Diffraction Pattern (revised 7/10)

  228. Diffraction Pattern for Two Concentric Rings (5/13)

  229. Density Operator Approach to the Double-Slit Experiment (4-08)

  230. Another Look at the Double-Slit Experiment

  231. A Quantum Mechanical Interpretation of Diffraction

  232. Electron Diffraction at Multiple Slits

  233. Multiple Slit Diffraction and the Fourier Transform (09/12)

  234. The Double-Slit Experiment with C60 Molecules

  235. Crystal Structure, Rotational Symmetry and Quasicrystals

  236. X-ray Crystallography from a Quantum Mechanical Perspective

  237. X-ray Diffaction (rev. 6/13)

  238. Holography Involves Single Photon Interference

    Return to top of page.

    Group Theory with Mathcad

  239. Group Theory Principles Applied to H2O (5/11)

  240. Dodecahedrane

  241. Xenon Tetrafluoride

  242. Diborane

  243. Cubane

  244. Buckminsterfulerene

  245. BCl3

  246. Ti(H2O)63+

  247. CH4

  248. P4

  249. Tetrahedrane (9/09)

  250. PH3 (9/09)

  251. Cyclopropane (9/09)

  252. An Extensive Set of Group Theory Problems for Chemists (8/10)

    Return to top of page

    Quantum Optics

  253. Single-Photon Interference - First version

  254. Single-Photon Interference - Second version

  255. Single-Photon Interference - Third version

  256. Single Photon Interference - Fourth version (revised 7/14)

  257. Single Photon Interference - Mathcad version

  258. The Polarizing Beam Splitter and the Superposition Principle (5/15)

  259. Mach-Zehnder Polarization Interferometer Analyzed Using Tensor Algegra (rev. 10/12)

  260. Illustrating the Superposition Principle with Single Photon Interference

  261. Pure States, Mixtures and the Density Operator

  262. Using the Trace Function to Calculate Expectation Values (4/17)

  263. Polarized Light and the Quantum Superposition (7/08)

  264. Polarized Light and Quantum Mechanics

  265. The Three-Polarizer Paradox (10/12)

  266. Matrix Mechanics Approach to Polarized Light

  267. Matrix Mechanics Approach to Polarized Light - Version 2 (revised 3/11)

  268. Matrix Mechanics Exercises Using Polarized Light (1/11)

  269. Polarized Light and Quantum Mechanics (PDF version)

  270. Neutron Interferometry with Polarized Spin States (7/08)

  271. Interaction Free Measurement: Seeing in the Dark (6/11)

  272. Quantum Seeing in the Dark: A Matrix-Tensor Analysis (7/11)

  273. Two Analyses of the Michelson Interferometer (6/11)

  274. A Quantum Circuit for a Michelson Interferometer (1/13)

  275. The Ramsey Atomic Interferometer (2/13)

  276. Optical Activity: A Quantum Perspective (12/12)

  277. A Quantum Optical Cheshire Cat (7/14)

  278. Two Photon Interference: The Creation of an Entangled Superposition

  279. Two-particle Interference for Bosons and Fermions (rev. 1/16)

  280. Analysis of a Two-photon Interferometer (8/10)

  281. Two-photon Interferometry (2/13)

  282. Another Two Photon Interference Experiment

  283. Quantum Correlations Illuminated with Tensor Algebra (11/10)

  284. Two Photon Entanglement - A Tensor Algebra Analysis (rev. 2/11)

  285. Two Photon Interference - Matrix Mechanics Approach (rev. 1/10)

  286. Two-electron Interference (7/07)

  287. Bosonic and Fermionic Photon Behavior at Beam Splitters (rev. 9/14)

  288. Bosonic and Fermionic Photon Behavior at Beam Splitters: A Tensor Algebra Analysis (11/10)

  289. Entangled Photons Can Behave Like Fermions (2/13)

  290. Analyzing Two-photon Interferometry Using Mathcad and Tensor Algebra (rev. 1/16)

  291. Analysis of a Two-photon Quantum Eraser (8/12)

  292. A Quantum Delayed-Choice Experiment?(12/12)

  293. A Quantum Delayed-Choice Experiment?(5/18)

  294. A Single Page Summary of Quantum Teleportation (1/17)

  295. Quantum Teleportation: A Brief Introduction (rev. 9/12)

  296. Quantum Teleportation at a Glance (rev. 9/12)

  297. Another Look at Quantum Teleportation (rev. 6/13)

  298. Teleportation Using Quantum Gates (revised 2/13)

  299. Another Example of Teleportation Using Quantum Gates (revised 2/13)

  300. Yet Another Quantum Teleportation Circuit (12/14)

  301. Quantum Teleportation: Another Look (11/14)

  302. A Quantum Teleportation Experiment for Undergraduates (7/16)

  303. A Simple Teleportation Exercise (10/16)

  304. Teleportation as a Quantum Computation (2/13)

  305. Quantum Teleportation: Four Perspectives (9/16)

  306. Clare Johnston's Teleportation Poster

  307. Teleportation of Two Qubits (rev. 1/17)

  308. Greenaberger-Horne-Zeilinger (GHZ) Entanglement and Local Realism (7/08)

  309. GHZ Entanglement: A Tensor Algebra Analysis (revised 2/11)

  310. Simulation of a GHZ Gedanken Experiment (1/18)

  311. Another Simulation of a GHZ Gedanken Experiment (7/18)

  312. A Surgical Refutation of the Local Realism Heresy (8/17))

  313. GHZ Four-Photon Entanglement Analyzed Using Tensor Algebra (revised 4/11)

  314. Quantum v. Realism (4/13)

  315. Elements of Reality: Another GHZ Gedanken Experiment Analyzed (revised 4/11)

  316. Brief Elements of Reality (7/18)

  317. A Brief Analysis of Mermin's GHZ Thought Experiment (7/11)

  318. Lucien Hardy's Paradox as Presented by N. David Mermin (2/11)

  319. Hardy's Paradox: An Algebraic Analysis (5/18)

  320. Quantum Entanglement Leads to Nonclassical Correlations (rev 1/16)

  321. Nonclassical Correlations Revealed with Mermin's Pentagram (revised 9/17)

  322. Spooky Action at a Distance: The EPR Experiment with Photons

  323. God Plays Dice: Quantum Principles Illustrated (Power Point Presentation 2/06)

  324. David Bohm's EPR Gedanken Experiment (12/12)

  325. An Extension of Bohm's EPR Experiment (1/16)

  326. A Surgical Adjudication of the Conflict Between Quantum Theory and Local Realism (6/16)

  327. A Brief Analysis of the Conflict Between Quantum Theory and Local Realism (2/17)

  328. Positronium Annihilation (rev. 1/16)

  329. Mermin's Version of Bohm's EPR Gedanken Experiment (8/14)

  330. A Concise Version of Mermin's EPR Gedanken Experiment (4/15)

  331. Abother Look at Mermin's EPR Gedanken Experiment (1/16)

  332. Mermin's Version of Bohm's EPR Gedanken Experiment Using Tensor Algebra (revised 6/12)

  333. A GHZ Gedanken Experiment Using Spatial Degrees of Freedom and Tensor Algebra (4/11)

  334. Another GHZ Example Using Spin-1/2 Particles (4/11)

  335. Entanglement Reveals a Conflict Between Local Realism and Quantum Theory (rev. 1/16)

  336. A Summary of Feynman's "Simulating Physics with Computers" (rev. 6/16)

  337. Another Summary of Feynman's "Simulating Physics with Computers" (1/17)

  338. Yet Another Assault on Local Realism (5/11)

  339. Yet Another Assault on Local Realism - A Matrix/Tensor Algebra Approach (8/11)

  340. Jim Baggott's Bell Theorem Analysis(6/15)

  341. Another Bell Theorem Analysis(9/15)

  342. Another Bell Theorem Analysis - Shorter Version(4/17)

  343. EPR Analysis for a Composite Singlet Spin System (10/15)

  344. EPR Analysis for a Composite Singlet Spin System - Short Version (4/17)

  345. Analysis of the Stern-Gerlach Experiment (12/14)

  346. Hardy's Paradox (6/11)

  347. Bell State Exercises (rev. 3/13)

  348. Expressing Bell and GHZ States in Vector Format Using Mathcad (4/13)

  349. Quantum Circuit for the Generation of GHZ States (5/16)

  350. A Brief Description of Aspect's Experiment (8/12)

  351. The Kochen-Specker Theorem Illustrated Using A Three-Qubit GHZ System (12/12)

  352. A Brief Introduction to Entanglement Swapping (4/18)

  353. An Entanglement Swapping Protocol (revised 1/16)

  354. Quantum Correlations Simplified (6/17)

  355. Simulating Quantum Correlations with a Quantum Computer (1/18)

  356. Quantum Computer Simulation of Photon Correlations (1/18)

  357. Quantum Correlations Illustrated with Photons (6/17)

  358. Examining the Local States of an Entangled Bipartate Superposition (3/18)

  359. A Brief Introduction to the Quantum Computer (5/15)

  360. A Very Simple Example of Parallel Quantum Computation (rev. 7/13)

  361. Another Simple Example of Parallel Quantum Computation (2/16)

  362. A Simple Solution to Deutsch's Problem (rev. 5/15)

  363. Another Example of Deutsch's Algorithm (2/16)

  364. Evaluating a Function Using a Quantum Circuit and a Demonstration of Parallel Computation (rev. 7/15)

  365. A Simple Quantum Circuit for Parallel Computation (2/17)

  366. An Illustration of the Deutsch-Jozsa Algorithm (rev. 5/15)

  367. Another Illustration of the Deutsch-Jozsa Algorithm (12/14)

  368. Aspects of Simon's Algorithm (2/15)

  369. Qubit Quantum Mechanics (12/10)

  370. Implementation of Deutsch's Algorithm Using Mathcad (revised 3/11)

  371. Using Quantum Gates to Create Superpositions and Entangled States (2/11)

  372. A Simple Quantum Computer (11/11)

  373. Solving Equations Using a Quantum Circuit (rev. 10/16)

  374. Introduction to Superdense Coding (rev. 1/15)

  375. The Discrete or Quantum Fourier Transform (6/13)

  376. Factoring Using Shor's Quantum Algorithm (rev. 10/16)

  377. Shor's Quantum Algorithm - A Summary (12/16)

  378. Simulating the Deutsch-Jozsa Algorithm with a Double-Slit Apparatus (7/13)

  379. Simulating a Quantum Computer with a Mach-Zehnder Interferometer(5/16)

  380. Quantum Restrictions on Cloning (rev. 1/17)

  381. Quantum Error Correction(1/15)

  382. Matrix Mechanics Analysis of the BB84 Key Distribution (12/14)

  383. The Quantum Math Behind Ekert's Key Distribution Scheme (3/17)

  384. A Shorter Version of the Quantum Math Behind Ekert's Key Distribution Scheme (3/17)

  385. Quantum Key Distribution Using a Mach-Zehnder Interferometer (5/15)

  386. Coding and Decoding Venus(1/16)

  387. Grover's Quantum Search Algorithm (7/15)

  388. Grover's Search Algorithm: Implementation for Two Items (1/18)

  389. Grover's Search Algorithm: Four-Card Monte (1/18)

    Return to top of page.

    Numerical Solutions for Schrödinger's Equation Using Mathcad

  390. Introduction to Numerical Solutions of Schrödinger's Equation Using Mathcad

  391. Particle in an Infinite Potential Well

  392. Particle in a Gravitational Field

  393. Particle in a One-dimensional Egg Carton

  394. Particle in a Finite Potential Well (rev. 9/12)

  395. Particle in a Semi-infinite Potential Well

  396. Particle in a Slanted Potential Well

  397. Numerical Solutions for a Particle in a V-shaped Potential Well (9/12)

  398. Numerical Solutions for the Harmonic Oscillator (rev. 9/12)

  399. Numerical Solutions for a Double-Minimum Potential Well (10/12)

  400. Numerical Solutions for the Quartic Oscillator (9/12)

  401. Numerical Solutions for the Morse Oscillator (rev. 9/12)

  402. Numerical Solutions for the Lennard-Jones Potential (10/12)

  403. Numerical Solutions for the Double Morse Potential (9/12)

  404. Particle in a Box with an Internal Barrier (rev 6/08)

  405. Another Look at the Particle in a Box with an Internal Barrier (6/08)

  406. Particle in a Box with Multiple Internal Barriers (6/08)

  407. Particle in an Infinite Spherical Potential Well

  408. Numerical Solutions for the Two-Dimensional Harmonic Oscillator

  409. Numerical Solutions for the Three-Dimensional Harmonic Oscillator

  410. Numerical Solutions for the Hydrogen Atom Radial Equation

  411. Numerical Solutions for a Modified Harmonic Potential (7/10)

    Return to top of page.

    Approximate Quantum Mechanical Methods

  412. Trial Wave Functions for Various Potentials

  413. Energy Minimization - Four Methods Using Mathcad (6/16)

  414. The Variation Theorem in Dirac Notation (3/09)

  415. A Rudimentary Model for Alpha Particle Decay (9/10)

  416. Variation Method for a Particle in a Finite Potential Well

  417. Variation Method for a Particle in a Symmetric 1D Potential Well

  418. Variation Method for the Rydberg Potential

  419. Variation Method for the Quartic Oscillator

  420. Momentum-Space Variation Method for the Quartic Oscillator

  421. Variation Method for a Particle in a Gravitational Field

  422. Variation Method for a Particle in a Slanted 1D Box

  423. Variation Method for a Particle in a Semi-infinite Potential Well

  424. Variation Method for a Particle in a Box with an Internal Barrier

  425. Variation Method for a Particle in a 1D Ice Cream Cone

  426. Variation Method for a Particle in an Ice Cream Cone

  427. Variation Method for a Particle in a Finite Spherical Potential Well

  428. Variation Method for the Harmonic Oscillator

  429. Trigonometric Trial Wave Function for the Harmonic Potential Well

  430. Trigonometric Trial Wave Function for the 3D Harmonic Potential Well

  431. Gaussian Trial Wave Function for the Hydrogen Atom

  432. Variation Calculation on the 1D Hydrogen Atom Using a Trigonometric Trial Wave Function (3/09)

  433. Variation Calculation on the 1D Hydrogen Atom Using a Gaussian Trial Wave Function (3/09)

  434. Variational Calculation on the Two-dimensional Hydrogen Atom (3/08)

  435. Variational Calculation on Helium Using a Hydrogenic Wave Function (2/08)

  436. Gaussian Trial Wave Function for the Helium Atom (12/07)

  437. Trigonometric Trial Wave Function for the Helium Atom (12/07)

  438. Trigonometric Trial Wave Function for the Hydrogen Atom

  439. Hydrogen Atom Calculation Assuming the Eelctron is a Particle in A Sphere of Radius R (12/07)

  440. Variational Calculations on the Lithium Atom

  441. The Variation Method in Momentum Space

  442. Momentum-Space Variation Method for Particle in a Gravitational Field

  443. Momentum-Space Variation Method for the Abs(x) Potential (2/08)

  444. Variational Method for the Feshbach Potential (6/08)

  445. Numerical Solution for the Feshbach Potential (6/08)

  446. First Order Degenerate Perturbation Theory: The Stark Effect for the Hydrogen Atom (2/08)

  447. Variational Calculation for the Polarizability of the Hydrogen Atom (5/08)

  448. Hybrid Variational Calculation for the 1D Hydrogen Atom with Delta Function Potential (rev. 4/16)

  449. Variation Method Using the Wigner Function: Finite Potential Well (12/08)

  450. Variation Method Using the Wigner Function: V(x) = |x| (12/08)

  451. Variation Method Using the Wigner Function: The Harmonic Oscillator (12/08)

  452. Variation Method Using the Wigner Function: The Quartic Oscillator (12/08)

  453. Variation Method Using the Wigner Function: The Feshbach Potential (12/08)

    Return to top of page.

    Miscellaneous

  454. The Art of Science (revised January 2006)

  455. Mass-Energy Equivalence

  456. Commentary on "Probing the Orbital Energy of an Electron in an Atom"

  457. The Use of Models in Introductory Chemistry

  458. Reaction to Gillespie's Six Great Ideas in Chemistry: Another Great Idea (revised 7/10)

  459. An Alternative Derivation of Gas Pressure Using the Kinetic Theory

  460. Examining Fourier Synthesis with Dirac Notation (revised 5/15)

  461. Finding Roots of Trancendental Equations

  462. Calculation of the Composition of a Weak Polyprotic Acid Using Mathcad

  463. Solving Linear Equations Using Mathcad

  464. Let's Teach High School Students Computer Algebra Methods (10/10)

  465. Thermodynamics and Kinetics

  466. Simple Kinetic Derivations of Thermodynamic Relations

  467. The Global Approach to Thermodynamics: Try It, You'll Like It! (6/08)

  468. Global Thermodynamic Analyses of Heat Engines (11/08)

  469. Using Charles' Law to Determine Absolute Zero (12/08)

  470. The Origin of KE = 3/2 RT (12/08)

  471. Determining the Temperature of the Cosmic Background Radiation

  472. Age of the Elements (3/13)

    Return to top of page.

    Back to Frank Rioux's homepage.