Quantum Tutorials

by Frank Rioux

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These tutorials complement many topics found in introductory and advanced quantum mechanism courses.

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Publisher
College of Saint Benedict/Saint John's University
Subjects
Chemistry, Physical and Theoretical Chemistry Textbook Maps
Licence
CC BY 4.0, as LibreTexts states it
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Tweens profiles and older, judged from its title and subjects

Contents

LibreTexts writes equations in TeX, and here they show as TeX; the PDF has them typeset.

  1. Front Matter
  2. TitlePage
  3. InfoPage
  4. Table of Contents
  5. Licensing
  6. 1: Quantum Fundamentals
  7. 1.1: An Approach to Quantum Mechanics
  8. 1.2: Atomic and Molecular Stability
  9. 1.3: Atomic and Molecular Stability
  10. 1.4: Atomic and Molecular Stability
  11. 1.5: Quantum Computation - A Short Course
  12. 1.6: Quantum Computation- A Short Course
  13. 1.7: Quantum Computation- A Short Course
  14. 1.8: Quantum Computation- A Short Course
  15. 1.9: Quantum Computation- A Short Course
  16. 1.100: Analysis of the Stern-Gerlach Experiment
  17. 1.101: Related Analysis of the Stern-Gerlach Experiment
  18. 1.103: Bloch Sphere
  19. 1.104: 88. Related Analysis of the Stern-Gerlach Experiment
  20. 1.105: Bill the Cat and the Superposition Principle
  21. 1.106: Schroedinger's Dog
  22. 1.107: The Bloch Sphere
  23. 1.108: Density Matrix, Bloch Vector and Entropy
  24. 1.109: State Vectors and State Operators- Superpositions, Mixed States, and Entanglement
  25. 1.10: Quantum Computation- A Short Course
  26. 1.110: The Gram-Schmidt Procedure
  27. 1.11: Quantum Computation- A Short Course
  28. 1.12: Quantum Computation- A Short Course
  29. 1.13: Quantum Mechanics and the Fourier Transform
  30. 1.14: Quantum Mechanics and the Fourier Transform
  31. 1.15: Quantum Mechanics and the Fourier Transform
  32. 1.16: Quantum Mechanics and the Fourier Transform
  33. 1.17: Quantum Mechanics and the Fourier Transform
  34. 1.18: Exploring the Origin of Schrödinger’s Equations
  35. 1.19: Basic Quantum Mechanics in Coordinate, Momentum and Phase Space
  36. 1.20: The Repackaging of Quantum Weirdness
  37. 1.21: Quantum Principles Illuminated with Polarized Light
  38. 1.22: Relationship Between the Coordinate and Momentum Representations
  39. 1.23: Very Brief Relationship Between the Coordinate and Momentum Representations
  40. 1.24: Getting Accustomed to the Superposition Principle
  41. 1.25: The Dirac Delta Function
  42. 1.26: Elements of Dirac Notation
  43. 1.27: The Dirac Notation Applied to Variational Calculations
  44. 1.28: Raising and Lowering; Creating and Annihilating
  45. 1.29: Single Slit Diffraction and the Fourier Transform
  46. 1.30: From Coordinate Space to Momentum Space and Back
  47. 1.31: The Position and Momentum Commutation Relation in Coordinate and Momentum Space
  48. 1.32: Simulating the Aharonov-Bohm Effect
  49. 1.33: Basic Matrix Mechanics
  50. 1.34: Rudimentary Matrix Mechanics
  51. 1.35: Matrix Mechanics
  52. 1.36: Aspects of Diracʹs Relativistic Matrix Mechanics
  53. 1.37: The Double-Slit Experiment
  54. 1.38: Double‐Slit Experiment with Polarized Light
  55. 1.39: The Consequences of Path Information in a Mach-Zehnder Interferometer
  56. 1.40: Another look at the Consequences of Path Information in a Mach-Zehnder Interferometer
  57. 1.41: The Double‐Slit Experiment with Polarized Light
  58. 1.42: The Quantum Eraser
  59. 1.43: Which Way Did It Go? ‐ The Quantum Eraser
  60. 1.44: Which Path Information and the Quantum Eraser
  61. 1.45: Terse Analysis of Triple-slit Diffraction with a Quantum Eraser
  62. 1.46: Which Path Information and the Quantum Eraser (Brief)
  63. 1.47: Terse Analysis of Triple-slit Diffraction with a Quantum Eraser
  64. 1.48: Which‐way Markers and Post‐selection in the Double‐slit Experiment
  65. 1.49: A Stern‐Gerlach Quantum ʺEraserʺ
  66. 1.50: Using the Mach-Zehnder Interferometer to Illustrate the Impact of Which-way Information
  67. 1.51: Quantum Theory, Wave-Particle Duality and the Mach-Zehnder Interferometer
  68. 1.52: Analysis of a Temporal Double-slit Experiment
  69. 1.53: An Analysis of Three‐Path Interference
  70. 1.54: An Analysis of Three-Slit Interference
  71. 1.55: Using a Mach-Zehnder Interferometer to Illustrate Feynman's Sum Over Histories Approach to Quantum Mechanics
  72. 1.56: The Paradox of Recombined Beams
  73. 1.57: Evidence for Quantized Gravitational States of the Neutron
  74. 1.58: Quantized Gravitational States A Variational Approach
  75. 1.59: The Quantum Bouncer Doesnʹt Bounce, Unless...
  76. 1.60: Kinetic Energy Is Important in the Nanoscale World
  77. 1.61: Energy Expectation Values and the Origin of the Variation Principle
  78. 1.62: Examining the Wigner Distribution Using Dirac Notation
  79. 1.63: The Wigner Function for the Single Slit Diffraction Problem
  80. 1.64: Wigner Distribution for the Double Slit Experiment
  81. 1.65: Wigner Distribution for the Triple Slit Experiment
  82. 1.66: Wigner Distribution for the Quadruple Slit Experiment
  83. 1.67: Quantum Tunneling in Coordinate, Momentum and Phase Space
  84. 1.68: Another Look at the Wigner Function
  85. 1.69: The Wigner Distribution Function for the Harmonic Oscillator
  86. 1.70: Wigner Distribution for the Particle in a Box
  87. 1.71: The Wigner Distribution for a Particle in a One‐dimensional Box
  88. 1.72: Superposition vs. Mixture
  89. 1.73: Time‐dependent Wigner Function for Harmonic Oscillator Transitions
  90. 1.74: Momentum Operator in Coordinate Space
  91. 1.75: Momentum Wave Functions for the Particle in a Box
  92. 1.76: A Graphical Illustration of the Heisenberg Uncertainty Relationship
  93. 1.77: The Quantum Harmonic Oscillator
  94. 1.78: Coherent Superpositions for the Harmonic Oscillator
  95. 1.79: The Harmonic Oscillator and the Uncertainty Principle
  96. 1.80: Another view of the Harmonic Oscillator and the Uncertainty Principle
  97. 1.81: Hydrogen Atom and Helium Ion Spatial and Momentum Distribution Functions Illustrate the Uncertainty Principle
  98. 1.82: The Position‐Momentum Uncertainty Relation in the Hydrogen Atom
  99. 1.83: Demonstrating the Uncertainty Priniciple for Angular Momentum and Angular Position
  100. 1.84: A Brief Tutorial on Wavepackets
  101. 1.85: The Difference Between Fermions and Bosons
  102. 1.86: Quantum Corrals - Electrons within a Ring
  103. 1.87: Planck's Radiation Equation Fit to Experimental Data
  104. 1.88: Planck's Radiation Equation Fit to Experimental Data - Another Algorithm
  105. 1.89: Fitting Einstein's Heat Capacity Equation to Experimental Data for Silver
  106. 1.90: Einstein's Heat Capacity Equation Fit to Experimental Data - Another Algorithm
  107. 1.91: Fitting Debye's Heat Capacity Equation to Experimental Data for Silver
  108. 1.92: Debye's Heat Capacity Equation Fit to Experimental Data - Another Algorithm
  109. 1.93: Wave-particle Duality and the Uncertainty Principle
  110. 1.94: Wave-Particle Duality for Matter and Light
  111. 1.95: What Part of the Quantum Theory Don’t You Understand?
  112. 1.96: Quantum Potpourri - An Attempt to Demonstrate Two Fundamental Quantum Concepts- Wave-particle Duality and The Superposition Principle
  113. 1.97: Quantum Dynamics- One Step at a Time
  114. 1.98: Quantum Mechanical Pressure
  115. 1.99: Visualizing the Difference Between a Superposition and a Mixture
  116. 2: Atomic Structure
  117. 2.1: The de Broglie-Bohr Model for the Hydrogen Atom
  118. 2.2: The de Broglie-Bohr Model for the Hydrogen Atom - Version 3
  119. 2.3: The de Broglie-Bohr Model for the Hydrogen Atom - Version 3
  120. 2.4: A de Broglie-Bohr Model for Positronium
  121. 2.5: The de Broglie-Bohr Model for the Hydrogen Atom - Version 4
  122. 2.6: The de Broglie-Bohr Model for a Hydrogen Atom Held Together by a Gravitational Interaction
  123. 2.7: The de Broglie-Bohr Model for Positronium
  124. 2.8: The Bohr Model for the Earth-Sun System
  125. 2.9: Extracting Atomic and Molecular Parameters from the deBroglie-Bohn Model for the Atom
  126. 2.10: Electronic Structure and the Superposition Principle
  127. 2.11: Atomic Spectroscopy and the Correspondence Principle
  128. 2.12: Hydrogen-Like Calculations with Variable Lepton Mass
  129. 2.13: Atomic Stability
  130. 2.14: Quantum Mechanical Calculations for the One-Dimensional Hydrogen Atom
  131. 2.15: Quantum Mechanical Calculations for the Hydrogen Atom
  132. 2.16: Atomic Stability
  133. 2.17: Atomic Stability - Mathcad Version
  134. 2.18: 110. Critique of the Centrifugal Effect in the Hydrogen Atom
  135. 2.19: A Shorter Critique of the Centrifugal Effect in the Hydrogen Atom
  136. 2.20: Exploring the Role of Lepton Mass in the Hydrogen Atom
  137. 2.21: The Effect of Lepton Mass on the Energy and Bond Length of the Hydrogen Molecule Ion
  138. 2.22: The Hydrogen Atom with Finite Sized Nucleus
  139. 2.23: The Hyperfine Interaction in the Hydrogen Atom
  140. 2.24: Positronium Annihilation
  141. 2.25: Positronium Annihilation- Another View
  142. 2.26: Positronium Annihilation- Yet Another View
  143. 2.27: The Hyperfine Interaction in the Deutrium Atom
  144. 2.28: A Tensor Algebra Approach to Spin-Orbit Coupling
  145. 2.29: A Bohr Model for Multi-electron Atoms and Ions
  146. 2.30: Atomic Variational Calculations- Hydrogen to Boron
  147. 2.31: Some Calculations on the Lithium Atom Ground State
  148. 2.32: E. B. Wilson's Calculation on the Lithium Atom Ground State
  149. 2.33: The Importance of the Pauli Principle
  150. 2.34: Splitting the 2s-2p Degeneracy in the Lithium Atom
  151. 2.35: Addition of Spin Angular Momentum- A Tensor Algebra Approach
  152. 2.36: Hund's Rule
  153. 2.37: Hund's Rule - Singlet-Triplet Calculations with Mathcad
  154. 2.38: Electron Correlation in Two-electron Systems
  155. 2.39: First Trial Wave Function
  156. 2.40: Second Trial Wavefunction
  157. 2.41: Third Trial Wavefunction
  158. 2.42: 129.4 Fourth Trial Wavefunction
  159. 2.43: Fifth Trial Wavefunction and Summary
  160. 2.44: The Crucial Role of Kinetic Energy in Interpreting Ionization Energies
  161. 2.45: Quantum Dots Are Artificial Atoms
  162. 2.46: Calculating the Atomic Radius of Polonium
  163. 2.47: Calculating the Atomic Radius of Gold
  164. 2.48: How Many Bibles Can Fit on the Head of a Pin
  165. 2.49: Momentum Wavefunctions and Distributions for the Hydrogen Atom
  166. 2.50: The SCF Method for Two Electrons
  167. 2.51: Outline of the SCF Method for Two Electrons
  168. 2.52: The SCF Method for Two Electrons Using a Gaussian Wave Function
  169. 2.53: An Interactive SCF Calculation for the Helium Atom
  170. 2.54: Quantum Calculations on the Hydrogen Atom in Coordinate, Momentum and Phase Space
  171. 2.55: The Wigner Distribution for the 1s State of the 1D Hydrogen Atom
  172. 2.56: The Wigner Distribution for the 2s State of the 1D Hydrogen Atom
  173. 2.57: The Wigner Distribution for the 2p State of the 1D Hydrogen Atom
  174. 2.58: The Wigner Distribution for the 3s State of the 1D Hydrogen Atom
  175. 2.59: The Wigner Distribution for the 3p State of the 1D Hydrogen Atom
  176. 2.60: The Wigner Distribution for the 4s State of the 1D Hydrogen Atom
  177. 2.61: One-dimensional H-atom with Delta Function Potential
  178. 2.62: The Atomic Structure Factor in Coordinate and Momentum Space
  179. 3: Chemical Bonding
  180. 3.1: The Covalent Bond and Quantum Mechanics
  181. 3.2: The Covalent Bond in the Hydrogen Molecule
  182. 3.3: The Covalent Bond Clarified Through the Use of the Virial Theorem
  183. 3.4: Brief Version of the Covalent Bond Clarified Through the Use of the Virial Theorem
  184. 3.5: The H2 Covalent Bond and the Virial Theorem
  185. 3.6: The Covalent Bond According to Slater and Ruedenberg
  186. 3.7: Slater's Analysis of the Covalent Bond using the Virial Theorem
  187. 3.8: Two Analyses of the Covalent Bond using the Virial Theorem
  188. 3.9: A Simple Charge Cloud Model for Molecular Hydrogen- Or, Is It a DFT Model?
  189. 3.10: Three Mechanisms for Bond Formation in the Hydrogen Molecule Ion
  190. 3.11: A Mechanistic Approach to Bond Formation in the Hydrogen Molecule Ion
  191. 3.12: A Lite Version of Ruedenberg's Analysis of the Covalent Bond in the Hydrogen Molecule Ion
  192. 3.13: Molecular Orbital Analysis for the Hydrogen Molecule Ion Bond
  193. 3.14: A One-dimensional Model for the Covalent Bond in the Hydrogen Molecule Ion
  194. 3.15: Localized and Delocalized Molecular Orbitals
  195. 3.16: Two Perspectives on the Bonding in Water
  196. 3.17: Covalent Bonding in Ammonia from Several Perspectives
  197. 3.18: A Molecular Orbital Approach to Bonding in Methane
  198. 3.19: A Simple Calculation of the Lattice Energy of LiH
  199. 3.20: An Even Simpler LiH Lattice Energy Calculation
  200. 3.21: Charge Cloud Models for Some Simple Atomic, Molecular and Solid Systems
  201. 3.22: A Critique of the Valence Shell Electron Pair Repulsion Model
  202. 3.23: A Simple Electrostatic Critique of VSEPR
  203. 3.24: Another Critique of VSEPR
  204. 3.25: Why Nonbonding Electrons Occupy the Equatorial Position in Trigonal Bipyramidal Geometry
  205. 3.26: A Modified Tangent Spheres Model Analysis of Trigonal Bipyramidal Geometry
  206. 3.27: A Symbolic Huckel MO Calculation Using Mathcad
  207. 3.28: A Numeric Huckel MO Calculation Using Mathcad
  208. 3.29: A Numerical Huckel MO Calculation on C60
  209. 3.30: Chemical Bonding and Electronic Structure of Buckminsterfullerene
  210. 3.31: Quantum Mechanics, Group Theory and C60
  211. 3.32: A Numerical Huckel Calculation on Anthracene and Phenanthrene
  212. 3.33: A Numerical Huckel Calculation on C10H8 Isomers
  213. 3.34: Semi-empirical Molecular Orbital Calculation on HF
  214. 3.35: Semi-empirical Molecular Orbital Calculation on XeF2
  215. 3.36: Posch-Teller Potential Model for Metals
  216. 4: Spectroscopy
  217. 4.1: Rudiments of Atomic Spectroscopy Using Mathcad
  218. 4.2: A Particle-in-a-Box Model for Color Centers
  219. 4.3: Cyanine Dyes as Two-State Electronic Systems
  220. 4.4: The Ammonia Inversion and the Maser
  221. 4.5: A Symmetric Double Well Potential Illustrating Tunneling
  222. 4.6: Analyses of the Pure Rotational Spectrum of HCl
  223. 4.7: A Rudimentary Analysis of the Vibrational-Rotational HCl Spectrum
  224. 4.8: Visualizing the Formally Forbidden Overtone Vibrational Transitions in HCl
  225. 4.9: The Quantum Jump
  226. 4.10: Another Look at the Quantum Jump
  227. 4.11: Quantum Beats
  228. 4.12: The 1s-2s Electronic Transition in the 1D Hydrogen Atom
  229. 4.13: The Quantum Jump in Momentum Space
  230. 4.14: The Harmonic Oscillator Quantum Jump
  231. 4.15: Coherent States of the Harmonic Oscillator
  232. 4.16: Analysis of the Electronic Spectrum of Ti(H2O)3+
  233. 4.17: Quantum Jumps for an Electron on a Ring
  234. 4.18: Analysis of the Vibrational and Electronic Spectrum of Benzene
  235. 4.19: NMR - Quantum Mechanics of a Three Proton System
  236. 4.20: AB Proton NMR Using Tensor Algebra
  237. 4.21: Calculating the AB Proton NMR Using Tensor Algebra
  238. 4.22: AB Proton NMR Analysis for 2,3-dibromothiophene
  239. 4.23: ABC Proton NMR Using Tensor Algebra
  240. 4.24: AB2 Proton NMR Using Tensor Algebra
  241. 4.25: AB3 Proton NMR Using Tensor Algebra
  242. 4.26: HD-Like NMR Spectrum Calculated Using Tensor Algebra
  243. 4.27: The Michelson Interferometer and Fourier Transform Spectroscopy
  244. 4.28: A Sum Over Histories Approach to Fourier Transform Infrared Spectroscopy
  245. 4.29: Modeling the Pi-electrons of Benzene as Particles on a Ring
  246. 4.30: Modeling the Pi-electrons of Benzene as Particles on a Ring - Version 2
  247. 4.31: Calculating the Pi-electron HOMO-LUMO Electronic Transition for Benzene
  248. 4.32: Modeling the Pi-electrons of Benzene as Particles in a Ring
  249. 4.33: Modeling the Pi-electrons of Corannulene as Particles in a Ring
  250. 4.34: The Vibrational and Electronic States of C60
  251. 5: Diffraction Phenomena
  252. 5.1: Using Optical Transforms to Teach Quantum Mechanics
  253. 5.2: Single-slit Diffraction and the Uncertainty Principle
  254. 5.3: Single-slit Diffraction and the Uncertainty Principle (Mathcad Version)
  255. 5.4: Simulating DNA's Diffraction Pattern
  256. 5.5: Simulating DNA's Diffraction Pattern with a More Realistic Model
  257. 5.6: Simulating DNA's Diffraction Pattern - Short Version
  258. 5.7: A Model Graphene Diffraction Pattern
  259. 5.8: Is a Two-dimensional Fibonacci Array a Quasilattice?
  260. 5.9: Calculating Diffraction Patterns
  261. 5.10: Modeling the C60 Diffraction Pattern
  262. 5.11: Diffraction Pattern for Pentagonal Point Scatterers
  263. 5.12: Diffraction Pattern for Pentagonal Finite Point Scatterers
  264. 5.13: Pentagram Diffraction Pattern
  265. 5.14: Model Diffraction Pattern for Napthalene
  266. 5.15: Calculating the Airy Diffraction Pattern
  267. 5.16: Diffraction Pattern for Two Concentric Rings
  268. 5.17: Density Operator Approach to the Double-Slit Experiment
  269. 5.18: Another Look at the Double-Slit Experiment
  270. 5.19: A Quantum Mechanical Interpretation of Diffraction
  271. 5.20: Electron Diffraction at Multiple Slits
  272. 5.21: Multiple Slit Diffraction and the Fourier Transform
  273. 5.22: The Double-Slit Experiment with C60 Molecules
  274. 5.23: Crystal Structure, Rotational Symmetry, and Quasicrystals
  275. 5.24: X-ray Crystallography from a Quantum Mechanical Perspective
  276. 5.25: Holography Involves Single Photon Interference
  277. 5.26: X-ray Diffraction
  278. 5.27: Holography Involves Single Photon Interference
  279. 6: Group Theory with Mathcad
  280. Front Matter
  281. TitlePage
  282. InfoPage
  283. 6.1: Group Theory Principles Applied to H2O
  284. 6.2: Dodecahedrane
  285. 6.3: Xenon Tetrafluoride
  286. 6.4: Diborane
  287. 6.5: Cubane
  288. 6.5.1: Buckminsterfulerene
  289. 6.6: BCl3
  290. 6.7: Ti(H2O)6 3+
  291. 6.8: CH₄
  292. 6.9: P₄
  293. 6.10: Tetrahedrane
  294. 6.11: PH3
  295. 6.12: Cyclopropane
  296. 6.13: An Extensive Set of Group Theory Problems for Chemists
  297. Back Matter
  298. Index
  299. 7: Quantum Optics
  300. Front Matter
  301. TitlePage
  302. InfoPage
  303. 7.1: Single-Photon Interference - First Version
  304. 7.2: Single-Photon Interference - Second Version
  305. 7.3: Single-photon Interference - Third Version
  306. 7.4: Single Photon Interference - Fourth Version
  307. 7.5: Single Photon Interference - Mathcad version
  308. 7.6: The Polarizing Beam Splitter and the Superposition Principle
  309. 7.7: Mach-Zehner Polarization Interferometer Analyzed Using Tensor Algebra
  310. 7.8: Illustrating the Superposition Principle with Single Photon Interference
  311. 7.9: Pure States, Mixtures and the Density Operator
  312. 7.10: Using the Trace Function to Calculate Expectation Values
  313. 7.11: Polarized Light and Quantum Superposition
  314. 7.12: Polarized Light and Quantum Mechanics
  315. 7.13: The Three-Polarizer Paradox
  316. 7.14: Matrix Mechanics Approach to Polarized Light
  317. 7.15: Matrix Mechanics Approach to Polarized Light - Version 2
  318. 7.16: Matrix Mechanics Exercises Using Polarized Light
  319. 7.17: Polarized Light and Quantum Mechanics
  320. 7.18: Neutron Interferometry with Polarized Spin States
  321. 7.19: Interaction Free Measurement - Seeing in the Dark
  322. 7.20: Quantum Seeing in the Dark - A Matrix-Tensor Analysis
  323. 7.21: Two Analyses of the Michelson Interferometer
  324. 7.22: A Quantum Circuit for a Michelson Interferometer
  325. 7.23: The Ramsey Atomic Interferometer
  326. 7.24: Optical Activity - A Quantum Perspective
  327. 7.25: A Quantum Optical Cheshire Cat
  328. 7.26: Two Photon Interference - The Creation of an Entangled Superposition
  329. 7.27: Two-particle Interference for Bosons and Fermions
  330. 7.28: Analysis of a Two-photon Interferometer
  331. 7.29: Two-photon Interferometry
  332. 7.29.1: Another Two Photon Interference Experiment
  333. 7.30: Another Two Photon Interference Experiment
  334. 7.31: Quantum Correlations Illuminated with Tensor Algebra
  335. 7.32: Two Photon Entanglement - A Tensor Algebra Analysis
  336. 7.33: Two Photon Interference - Matrix Mechanics Approach
  337. 7.34: Two-electron Interference
  338. 7.35: Bosonic and Fermionic Photon Behavior at Beam Splitters
  339. 7.36: Bosonic and Fermionic Photon Behavior at Beam Splitters- A Tensor Algebra Analysis
  340. 7.37: Entangled Photons Can Behave Like Fermions
  341. 7.38: Analyzing Two-photon Interferometry Using Mathcad and Tensor Algebra
  342. 7.39: Analysis of a Two-photon Quantum Eraser
  343. 7.40: Another Example of a Two-photon Quantum Eraser
  344. 7.41: A Quantum Delayed-Choice Experiment
  345. 7.42: A Quantum Delayed-Choice Experiment
  346. Back Matter
  347. Index
  348. 8: Quantum Teleportation
  349. 8.1: A Single Page Summary of Quantum Teleportation
  350. 8.2: Quantum Teleportation - A Brief Introduction
  351. 8.3: Quantum Teleportation at a Glance
  352. 8.4: Another Look at Quantum Teleportation
  353. 8.5: Teleportation Using Quantum Gates
  354. 8.6: Another Example of Teleportation Using Quantum Gates
  355. 8.7: Yet Another Quantum Teleportation Circuit
  356. 8.8: Quantum Teleportation - Another Look
  357. 8.9: A Quantum Teleportation Experiment for Undergraduates
  358. 8.10: A Simple Teleportation Exercise
  359. 8.11: Teleportation as a Quantum Computation
  360. 8.12: Quantum Teleportation - Four Perspectives
  361. 8.13: Teleportation of Two Qubits
  362. 8.14: Greenaberger-Hrne-Zeilinger (GHZ) Entanglement and Local Realism
  363. 8.15: GHZ Math Appendix
  364. 8.16: GHZ Entanglement - A Tensor Algebra Analysis
  365. 8.17: Simulation of a GHZ Gedanken Experiment
  366. 8.18: Another Simulation of a GHZ Gedanken Experiment
  367. 8.19: A Surgical Refutation of the Local Realism Heresy
  368. 8.20: GHZ Four-Photon Entanglement Analyzed Using Tensor Algebra
  369. 8.21: Quantum v. Realism
  370. 8.22: Elements of Reality- Another GHZ Gedanken Experiment Analyzed
  371. 8.23: Brief Elements of Reality
  372. 8.24: A Brief Analysis of Mermin's GHZ Thought Experiment
  373. 8.25: Lucien Hardy's Paradox as Presented by N. David Mermin
  374. 8.26: Hardy's Paradox - An Algebraic Analysis
  375. 8.27: Quantum Entanglement Leads to Nonclassical Correlations
  376. 8.28: Nonclassial Correlations Revealed with Mermin's Pentagram
  377. 8.29: Spooky Action at a Distance- The EPR Experiment with Photons
  378. 8.30: David Bohm's EPR Gedanken Experiment
  379. 8.31: An Extension of Bohm's EPR Experiment
  380. 8.32: A Surgical Adjudication of the Conflict Between Quantum Theory and Local Realism
  381. 8.33: A Thought Experiment Reveals the Conflict Between Quantum Theory and Local Realism
  382. 8.34: Positronium Annihilation
  383. 8.35: Mermin's Version of Bohm's EPR Gedanken Experiment
  384. 8.36: A Concise Version of Mermin's EPR Gedanken Experiment
  385. 8.37: Another Look at Mermin's EPR Gedanken Experiment
  386. 8.38: Mermin's Version of Bohm's EPR Gedanken Experiment Using Tensor Algebra
  387. 8.39: A GHZ Gedanken Experiment Using Spatial Degrees of Freedom and Tensor Algebra
  388. 8.40: Another GHZ Example Using Spin-1/2 Particles
  389. 8.41: Entanglement Reveals a Conflict Between Local Realism and Quantum Theory
  390. 8.42: A Summary of Feynman's "Simulating Physics with Computers"
  391. 8.43: Another Summary of Fenyman's "Stimulating Physics with Computers"
  392. 8.44: Yet Another Assault on Local Realism
  393. 8.45: Yet Another Assault on Local Realism - A Matrix/Tensor Algebra Approach
  394. 8.46: Jim Baggott's Bell Theorem Analysis
  395. 8.47: Another Bell Theorem Analysis
  396. 8.48: Another Bell Theorem Analysis - Shorter Version
  397. 8.49: EPR Analysis for a Composite Singlet Spin System
  398. 8.50: EPR Analysis for a Composite Singlet Spin System - Short Version
  399. 8.51: Analysis of the Stern-Gerlach Experiment
  400. 8.52: Hardy's Paradox
  401. 8.53: Bell State Exercises
  402. 8.54: Expressing Bell and GHZ States in Vector Format Using Mathcad
  403. 8.55: Quantum Circuit for the Generation of GHZ States
  404. 8.56: A Brief Description of Aspect's Experiment
  405. 8.57: The Kochen-Specker Theorem Illustrated Using a Three-Qubit GHZ System
  406. 8.58: A Brief Introduction to Entanglement Swapping
  407. 8.59: An Entanglement Swapping Protocol
  408. 8.60: Quantum Correlations Simplified
  409. 8.61: Simulating Quantum Correlations with a Quantum Computer
  410. 8.62: Quantum Computer Simulation of Photon Correlations
  411. 8.63: Quantum Correlations Illustrated with Photons
  412. 8.64: Examining the Local States of an Entangled Bipartate Superposition
  413. 8.65: A Brief Introduction to the Quantum Computer
  414. 8.66: A Very Simple Example of Parallel Quantum Computation
  415. 8.67: Another Simple Example of Parallel Quantum Computation
  416. 8.68: A Simple Solution to Deutsch's Problem
  417. 8.69: Another Example of Deutsch's Algorithm
  418. 8.70: Evaluating a Function Using a Quantum Circuit and a Demonstration of Parallel Computation
  419. 8.71: A Simple Quantum Circuit for Parallel Computation
  420. 8.72: An Illustration of the Deutsch-Jozsa Algorithm
  421. 8.73: Another Illustration of the Deutsch-Jozsa Algorithm
  422. 8.74: Aspects of Simon's Algorithm
  423. 8.75: Qubit Quantum Mechanics
  424. 8.76: Implementation of Deutsch's Algorithm Using Mathcad
  425. 8.77: Using Quantum Gates to Create Superpositions and Entangled States
  426. 8.78: A Simple Quantum Computer
  427. 8.79: Solving Equations Using a Quantum Circuit
  428. 8.80: Introduction to Superdense Coding
  429. 8.81: A Brief Introduction to Quantum Dense Coding
  430. 8.82: The Discrete or Quantum Fourier Transform
  431. 8.83: Factoring Using Shor's Quantum Algorithm
  432. 8.84: Shor's Quantum Algorithm - A Summary
  433. 8.85: Simulating the Deutsch-Jozsa Algorithm with a Double-Slit Apparatus
  434. 8.86: Simulating a Quantum Computer with a Mach-Zehnder Interferometer
  435. 8.87: Quantum Restrictions on Cloning
  436. 8.88: Quantum Error Correction
  437. 8.89: Matrix Mechanics Analysis of the BB84 Key Distribution
  438. 8.90: 388. The Quantum Math Behind Ekert's Key Distribution Scheme
  439. 8.91: A Shorter Version of the Quantum Math Behind Ekert's Key Distribution Scheme
  440. 8.92: Quantum Key Distribution Using a Mach-Zehnder Interferometer
  441. 8.93: Coding and Decoding Venus
  442. 8.94: Grover's Quantum Search Algorithm
  443. 8.95: Grover's Search Algorithm- Implementation for Two Items
  444. 8.96: Grover's Search Algorithm- Four-Card Monte
  445. 9: Numerical Solutions for Schrödinger's Equation
  446. 9.1: Introduction to Numerical Solutions of Schödinger's Equation
  447. 9.2: Particle in an Infinite Potential Well
  448. 9.3: Particle in a Gravitational Field
  449. 9.4: Particle in a One-dimensional Egg Carton
  450. 9.5: Particle in a Finite Potential Well
  451. 9.6: Particle in a Semi-infinite Potential Well
  452. 9.7: Particle in a Slanted Well Potential
  453. 9.8: Numerical Solutions for a Particle in a V-Shaped Potential Well
  454. 9.9: Numerical Solutions for the Harmonic Oscillator
  455. 9.10: Numerical Solutions for a Double-Minimum Potential Well
  456. 9.11: Numerical Solutions for the Quartic Oscillator
  457. 9.12: Numerical Solutions for Morse Oscillator
  458. 9.13: Numerical Solutions for the Lennard-Jones Potential
  459. 9.14: Numerical Solutions for the Double Morse Potential
  460. 9.15: Particle in a Box with an Internal Barrier
  461. 9.16: Another Look at the in a Box with an Internal Barrier
  462. 9.17: Particle in a Box with Multiple Internal Barriers
  463. 9.18: Particle in an Infinite Spherical Potential Well
  464. 9.19: Numerical Solutions for the Two-Dimensional Harmonic Oscillator
  465. 9.20: Numerical Solutions for the Three-Dimensional Harmonic Oscillator
  466. 9.21: Numerical Solutions for the Hydrogen Atom Radial Equation
  467. 9.22: Numerical Solutions for a Modified Harmonic Potential
  468. 10: Approximate Quantum Mechanical Methods
  469. 10.1: Trial Wavefunctions for Various Potentials
  470. 10.2: Energy Minimization - Four Methods Using Mathcad
  471. 10.3: The Variation Theorem in Dirac Notation
  472. 10.4: A Rudimentary Model for Alpha Particle Decay
  473. 10.5: Variational Method for a Particle in a Finite Potential Well
  474. 10.6: Variation Method for a Particle in a Symmetric 1D Potential Well
  475. 10.7: Variation Method for the Rydberg Potential
  476. 10.8: Variation Method for the Quartic Oscillator
  477. 10.9: Momentum-Space Variation Method for the Quartic Oscillator
  478. 10.10: Variation Method for a Particle in a Gravitational Field
  479. 10.11: Linear Variational Method for a Particle in a Slanted 1D Box
  480. 10.12: Variation Method for a Particle in a Semi-Infinite Potential Well
  481. 10.13: Variation Method for a Particle in a Box with an Internal Barrier
  482. 10.14: Variation Method for a Particle in a 1D Ice Cream Cone
  483. 10.15: Variation Method for a Particle in an Ice Cream Cone
  484. 10.16: Variation Method for a Particle in a Finite 3D Spherical Potential Well
  485. 10.17: Variation Method for the Harmonic Oscillator
  486. 10.18: Trigonometric Trial Wave Function for the Harmonic Potential Well
  487. 10.19: Trigonometric Trial Wave Function for the 3D Harmonic Potential Well
  488. 10.20: Gaussian Trial Wavefunction for the Hydrogen Atom
  489. 10.21: Variation Calculation on the 1D Hydrogen Atom Using a Trigonometric Trial Wave Function
  490. 10.22: Variation Calculation on the 1D Hydrogen Atom Using a Gaussian Trial Wavefunction
  491. 10.23: Variational Calculation on the Two-dimensional Hydrogen Atom
  492. 10.24: Variational Calculation on Helium Using a Hydrogenic Wavefunction
  493. 10.25: Gaussian Trial Wave Function for the Helium Atom
  494. 10.26: Trigonometric Trial Wavefunction for the Helium Atom
  495. 10.27: Trigonometric Trial Wavefunction for the Hydrogen Atom
  496. 10.28: Hydrogen Atom Calculation Assuming the Electron is a Particle in a Sphere of Radius R
  497. 10.29: Electronic Structure - Variational Calculations on the Lithium Atom
  498. 10.30: The Variation Method in Momentum Space
  499. 10.31: Momentum-Space Variation Method for Particle in a Gravitational Field
  500. 10.32: Momentum-Space Variation Method for the Abs(x) Potential
  501. 10.33: Variational Method for the Feshbach Potential
  502. 10.34: Numerical Solution for the Feshbach Potential
  503. 10.35: First Order Degenerate Perturbation Theory - the Stark Effect of the Hydrogen Atom
  504. 10.36: Variational Calculation for the Polarizability of the Hydrogen Atom
  505. 10.37: Hybrid Variational Calculation for the 1D Hydrogen Atom with Delta Function Potential
  506. 10.38: Variation Method Using the Wigner Function- Finite Potential Well
  507. 10.39: 455. Variation Method Using the Wigner Function- V(x) = |x|
  508. 10.40: Variation Method Using the Wigner Function- The Harmonic Oscillator
  509. 10.41: Variation Method Using the Wigner Function - The Quartic Oscillator
  510. 10.42: Variation Method Using the Wigner Function - The Feshbach Potential
  511. 11: Miscellaneous
  512. 11.1: The Art of Science
  513. 11.2: Mass-Energy Equivalence
  514. 11.3: Commentary on “Probing the Orbital Energy of an Electron in an Atom”
  515. 11.4: The Use of Models in Introductory Chemistry
  516. 11.5: Reaction to Gillespie's Six Great Ideas in Chemistry - Another Great Idea
  517. 11.6: An Alternative Derivation of Gas Pressure Using the Kinetic Theory
  518. 11.7: Examining Fourier Synthesis with Dirac Notation
  519. 11.8: Finding Roots of Transcendental Equations
  520. 11.9: Calculation of the Composition of a Weak Polyprotic Acid Using Mathcad
  521. 11.10: Solving Linear Equations Using Mathcad
  522. 11.11: Let's Teach High School Students Computer Algebra Methods
  523. 11.12: Thermodynamics and Kinetics
  524. 11.13: Simple Kinetic Derivations of Thermodynamic Relations
  525. 11.14: The Global Approach to Thermodynamics
  526. 11.15: Global Thermodynamic Analyses of Heat Engines
  527. 11.16: Using Charles' Law to Determine Absolute Zero
  528. 11.17: The Origin of KE = 3/2 RT
  529. 11.18: Cosmic Background Radiation
  530. 11.19: Age of the Elements
  531. Back Matter
  532. Index
  533. Detailed Licensing