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Quantum Tutorials

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

Physical and Theoretical Chemistry Textbook Maps Chemistry

Author: Frank Rioux
Publisher: College of Saint Benedict/Saint John's University
Source: LibreTexts
License: CC BY
Language: EN
Category: Basic Sciences

Read online Download PDF (open licence)

Contents· 515 sections

01: Quantum Fundamentals
1.01: An Approach to Quantum Mechanics
1.02: Atomic and Molecular Stability
1.03: Atomic and Molecular Stability
1.04: Atomic and Molecular Stability
1.05: Quantum Computation - A Short Course
1.06: Quantum Computation- A Short Course
1.07: Quantum Computation- A Short Course
1.08: Quantum Computation- A Short Course
1.09: Quantum Computation- A Short Course
1.10: Quantum Computation- A Short Course
1.11: Quantum Computation- A Short Course
1.12: Quantum Computation- A Short Course
1.13: Quantum Mechanics and the Fourier Transform
1.14: Quantum Mechanics and the Fourier Transform
1.15: Quantum Mechanics and the Fourier Transform
1.16: Quantum Mechanics and the Fourier Transform
1.17: Quantum Mechanics and the Fourier Transform
1.18: Exploring the Origin of Schrodingers Equations
1.19: Basic Quantum Mechanics in Coordinate Momentum and Phase Space
1.20: The Repackaging of Quantum Weirdness
1.21: Quantum Principles Illuminated with Polarized Light
1.22: Relationship Between the Coordinate and Momentum Representations
1.23: Very Brief Relationship Between the Coordinate and Momentum Representations
1.24: Getting Accustomed to the Superposition Principle
1.25: The Dirac Delta Function
1.26: Elements of Dirac Notation
1.27: The Dirac Notation Applied to Variational Calculations
1.28: Raising and Lowering Creating and Annihilating
1.29: Single Slit Diffraction and the Fourier Transform
1.30: From Coordinate Space to Momentum Space and Back
1.31: The Position and Momentum Commutation Relation in Coordinate and Momentum Space
1.32: Simulating the Aharonov-Bohm Effect
1.33: Basic Matrix Mechanics
1.34: Rudimentary Matrix Mechanics
1.35: Matrix Mechanics
1.36: Aspects of Diracs Relativistic Matrix Mechanics
1.37: The Double-Slit Experiment
1.38: DoubleSlit Experiment with Polarized Light
1.39: The Consequences of Path Information in a Mach-Zehnder Interferometer
1.40: Another look at the Consequences of Path Information in a Mach-Zehnder Interferometer
1.41: The DoubleSlit Experiment with Polarized Light
1.42: The Quantum Eraser
1.43: Which Way Did It Go The Quantum Eraser
1.44: Which Path Information and the Quantum Eraser
1.45: Terse Analysis of Triple-slit Diffraction with a Quantum Eraser
1.46: Which Path Information and the Quantum Eraser (Brief)
1.47: Terse Analysis of Triple-slit Diffraction with a Quantum Eraser
1.48: Whichway Markers and Postselection in the Doubleslit Experiment
1.49: A SternGerlach Quantum Eraser
1.50: Using the Mach-Zehnder Interferometer to Illustrate the Impact of Which-way Information
1.51: Quantum Theory Wave-Particle Duality and the Mach-Zehnder Interferometer
1.52: Analysis of a Temporal Double-slit Experiment
1.53: An Analysis of ThreePath Interference
1.54: An Analysis of Three-Slit Interference
1.55: Using a Mach-Zehnder Interferometer to Illustrate Feynman's Sum Over Histories Approach to Quantum Mechanics
1.56: The Paradox of Recombined Beams
1.57: Evidence for Quantized Gravitational States of the Neutron
1.58: Quantized Gravitational States A Variational Approach
1.59: The Quantum Bouncer Doesnt Bounce Unless...
1.60: Kinetic Energy Is Important in the Nanoscale World
1.61: Energy Expectation Values and the Origin of the Variation Principle
1.62: Examining the Wigner Distribution Using Dirac Notation
1.63: The Wigner Function for the Single Slit Diffraction Problem
1.64: Wigner Distribution for the Double Slit Experiment
1.65: Wigner Distribution for the Triple Slit Experiment
1.66: Wigner Distribution for the Quadruple Slit Experiment
1.67: Quantum Tunneling in Coordinate Momentum and Phase Space
1.68: Another Look at the Wigner Function
1.69: The Wigner Distribution Function for the Harmonic Oscillator
1.70: Wigner Distribution for the Particle in a Box
1.71: The Wigner Distribution for a Particle in a Onedimensional Box
1.72: Superposition vs. Mixture
1.73: Timedependent Wigner Function for Harmonic Oscillator Transitions
1.74: Momentum Operator in Coordinate Space
1.75: Momentum Wave Functions for the Particle in a Box
1.76: A Graphical Illustration of the Heisenberg Uncertainty Relationship
1.77: The Quantum Harmonic Oscillator
1.78: Coherent Superpositions for the Harmonic Oscillator
1.79: The Harmonic Oscillator and the Uncertainty Principle
1.80: Another view of the Harmonic Oscillator and the Uncertainty Principle
1.81: Hydrogen Atom and Helium Ion Spatial and Momentum Distribution Functions Illustrate the Uncertainty Principle
1.82: The PositionMomentum Uncertainty Relation in the Hydrogen Atom
1.83: Demonstrating the Uncertainty Priniciple for Angular Momentum and Angular Position
1.84: A Brief Tutorial on Wavepackets
1.85: The Difference Between Fermions and Bosons
1.86: Quantum Corrals - Electrons within a Ring
1.87: Planck's Radiation Equation Fit to Experimental Data
1.88: Planck's Radiation Equation Fit to Experimental Data - Another Algorithm
1.89: Fitting Einstein's Heat Capacity Equation to Experimental Data for Silver
1.90: Einstein's Heat Capacity Equation Fit to Experimental Data - Another Algorithm
1.91: Fitting Debye's Heat Capacity Equation to Experimental Data for Silver
1.92: Debye's Heat Capacity Equation Fit to Experimental Data - Another Algorithm
1.93: Wave-particle Duality and the Uncertainty Principle
1.94: Wave-Particle Duality for Matter and Light
1.95: What Part of the Quantum Theory Dont You Understand
1.96: Quantum Potpourri - An Attempt to Demonstrate Two Fundamental Quantum Concepts- Wave-particle Duality and The Superposition Principle
1.97: Quantum Dynamics- One Step at a Time
1.98: Quantum Mechanical Pressure
1.99: Visualizing the Difference Between a Superposition and a Mixture
1.100: Analysis of the Stern-Gerlach Experiment
1.101: Related Analysis of the Stern-Gerlach Experiment
1.103: Bloch Sphere
1.104: 88. Related Analysis of the Stern-Gerlach Experiment
1.105: Bill the Cat and the Superposition Principle
1.106: Schroedinger's Dog
1.107: The Bloch Sphere
1.108: Density Matrix Bloch Vector and Entropy
1.109: State Vectors and State Operators- Superpositions Mixed States and Entanglement
1.110: The Gram-Schmidt Procedure
02: Atomic Structure
2.01: The de Broglie-Bohr Model for the Hydrogen Atom
2.02: The de Broglie-Bohr Model for the Hydrogen Atom - Version 3
2.03: The de Broglie-Bohr Model for the Hydrogen Atom - Version 3
2.04: A de Broglie-Bohr Model for Positronium
2.05: The de Broglie-Bohr Model for the Hydrogen Atom - Version 4
2.06: The de Broglie-Bohr Model for a Hydrogen Atom Held Together by a Gravitational Interaction
2.07: The de Broglie-Bohr Model for Positronium
2.08: The Bohr Model for the Earth-Sun System
2.09: Extracting Atomic and Molecular Parameters from the deBroglie-Bohn Model for the Atom
2.10: Electronic Structure and the Superposition Principle
2.11: Atomic Spectroscopy and the Correspondence Principle
2.12: Hydrogen-Like Calculations with Variable Lepton Mass
2.13: Atomic Stability
2.14: Quantum Mechanical Calculations for the One-Dimensional Hydrogen Atom
2.15: Quantum Mechanical Calculations for the Hydrogen Atom
2.16: Atomic Stability
2.17: Atomic Stability - Mathcad Version
2.18: 110. Critique of the Centrifugal Effect in the Hydrogen Atom
2.19: A Shorter Critique of the Centrifugal Effect in the Hydrogen Atom
2.20: Exploring the Role of Lepton Mass in the Hydrogen Atom
2.21: The Effect of Lepton Mass on the Energy and Bond Length of the Hydrogen Molecule Ion
2.22: The Hydrogen Atom with Finite Sized Nucleus
2.23: The Hyperfine Interaction in the Hydrogen Atom
2.24: Positronium Annihilation
2.25: Positronium Annihilation- Another View
2.26: Positronium Annihilation- Yet Another View
2.27: The Hyperfine Interaction in the Deutrium Atom
2.28: A Tensor Algebra Approach to Spin-Orbit Coupling
2.29: A Bohr Model for Multi-electron Atoms and Ions
2.30: Atomic Variational Calculations- Hydrogen to Boron
2.31: Some Calculations on the Lithium Atom Ground State
2.32: E. B. Wilson's Calculation on the Lithium Atom Ground State
2.33: The Importance of the Pauli Principle
2.34: Splitting the 2s-2p Degeneracy in the Lithium Atom
2.35: Addition of Spin Angular Momentum- A Tensor Algebra Approach
2.36: Hund's Rule
2.37: Hund's Rule - Singlet-Triplet Calculations with Mathcad
2.38: Electron Correlation in Two-electron Systems
2.39: First Trial Wave Function
2.40: Second Trial Wavefunction
2.41: Third Trial Wavefunction
2.42: 129.4 Fourth Trial Wavefunction
2.43: Fifth Trial Wavefunction and Summary
2.44: The Crucial Role of Kinetic Energy in Interpreting Ionization Energies
2.45: Quantum Dots Are Artificial Atoms
2.46: Calculating the Atomic Radius of Polonium
2.47: Calculating the Atomic Radius of Gold
2.48: How Many Bibles Can Fit on the Head of a Pin
2.49: Momentum Wavefunctions and Distributions for the Hydrogen Atom
2.50: The SCF Method for Two Electrons
2.51: Outline of the SCF Method for Two Electrons
2.52: The SCF Method for Two Electrons Using a Gaussian Wave Function
2.53: An Interactive SCF Calculation for the Helium Atom
2.54: Quantum Calculations on the Hydrogen Atom in Coordinate Momentum and Phase Space
2.55: The Wigner Distribution for the 1s State of the 1D Hydrogen Atom
2.56: The Wigner Distribution for the 2s State of the 1D Hydrogen Atom
2.57: The Wigner Distribution for the 2p State of the 1D Hydrogen Atom
2.58: The Wigner Distribution for the 3s State of the 1D Hydrogen Atom
2.59: The Wigner Distribution for the 3p State of the 1D Hydrogen Atom
2.60: The Wigner Distribution for the 4s State of the 1D Hydrogen Atom
2.61: One-dimensional H-atom with Delta Function Potential
2.62: The Atomic Structure Factor in Coordinate and Momentum Space
03: Chemical Bonding
3.01: The Covalent Bond and Quantum Mechanics
3.02: The Covalent Bond in the Hydrogen Molecule
3.03: The Covalent Bond Clarified Through the Use of the Virial Theorem
3.04: Brief Version of the Covalent Bond Clarified Through the Use of the Virial Theorem
3.05: The H2 Covalent Bond and the Virial Theorem
3.06: The Covalent Bond According to Slater and Ruedenberg
3.07: Slater's Analysis of the Covalent Bond using the Virial Theorem
3.08: Two Analyses of the Covalent Bond using the Virial Theorem
3.09: A Simple Charge Cloud Model for Molecular Hydrogen- Or Is It a DFT Model
3.10: Three Mechanisms for Bond Formation in the Hydrogen Molecule Ion
3.11: A Mechanistic Approach to Bond Formation in the Hydrogen Molecule Ion
3.12: A Lite Version of Ruedenberg's Analysis of the Covalent Bond in the Hydrogen Molecule Ion
3.13: Molecular Orbital Analysis for the Hydrogen Molecule Ion Bond
3.14: A One-dimensional Model for the Covalent Bond in the Hydrogen Molecule Ion
3.15: Localized and Delocalized Molecular Orbitals
3.16: Two Perspectives on the Bonding in Water
3.17: Covalent Bonding in Ammonia from Several Perspectives
3.18: A Molecular Orbital Approach to Bonding in Methane
3.19: A Simple Calculation of the Lattice Energy of LiH
3.20: An Even Simpler LiH Lattice Energy Calculation
3.21: Charge Cloud Models for Some Simple Atomic Molecular and Solid Systems
3.22: A Critique of the Valence Shell Electron Pair Repulsion Model
3.23: A Simple Electrostatic Critique of VSEPR
3.24: Another Critique of VSEPR
3.25: Why Nonbonding Electrons Occupy the Equatorial Position in Trigonal Bipyramidal Geometry
3.26: A Modified Tangent Spheres Model Analysis of Trigonal Bipyramidal Geometry
3.27: A Symbolic Huckel MO Calculation Using Mathcad
3.28: A Numeric Huckel MO Calculation Using Mathcad
3.29: A Numerical Huckel MO Calculation on C60
3.30: Chemical Bonding and Electronic Structure of Buckminsterfullerene
3.31: Quantum Mechanics Group Theory and C60
3.32: A Numerical Huckel Calculation on Anthracene and Phenanthrene
3.33: A Numerical Huckel Calculation on C10H8 Isomers
3.34: Semi-empirical Molecular Orbital Calculation on HF
3.35: Semi-empirical Molecular Orbital Calculation on XeF2
3.36: Posch-Teller Potential Model for Metals
04: Spectroscopy
4.01: Rudiments of Atomic Spectroscopy Using Mathcad
4.02: A Particle-in-a-Box Model for Color Centers
4.03: Cyanine Dyes as Two-State Electronic Systems
4.04: The Ammonia Inversion and the Maser
4.05: A Symmetric Double Well Potential Illustrating Tunneling
4.06: Analyses of the Pure Rotational Spectrum of HCl
4.07: A Rudimentary Analysis of the Vibrational-Rotational HCl Spectrum
4.08: Visualizing the Formally Forbidden Overtone Vibrational Transitions in HCl
4.09: The Quantum Jump
4.10: Another Look at the Quantum Jump
4.11: Quantum Beats
4.12: The 1s-2s Electronic Transition in the 1D Hydrogen Atom
4.13: The Quantum Jump in Momentum Space
4.14: The Harmonic Oscillator Quantum Jump
4.15: Coherent States of the Harmonic Oscillator
4.16: Analysis of the Electronic Spectrum of Ti(H2O)3
4.17: Quantum Jumps for an Electron on a Ring
4.18: Analysis of the Vibrational and Electronic Spectrum of Benzene
4.19: NMR - Quantum Mechanics of a Three Proton System
4.20: AB Proton NMR Using Tensor Algebra
4.21: Calculating the AB Proton NMR Using Tensor Algebra
4.22: AB Proton NMR Analysis for 23-dibromothiophene
4.23: ABC Proton NMR Using Tensor Algebra
4.24: AB2 Proton NMR Using Tensor Algebra
4.25: AB3 Proton NMR Using Tensor Algebra
4.26: HD-Like NMR Spectrum Calculated Using Tensor Algebra
4.27: The Michelson Interferometer and Fourier Transform Spectroscopy
4.28: A Sum Over Histories Approach to Fourier Transform Infrared Spectroscopy
4.29: Modeling the Pi-electrons of Benzene as Particles on a Ring
4.30: Modeling the Pi-electrons of Benzene as Particles on a Ring - Version 2
4.31: Calculating the Pi-electron HOMO-LUMO Electronic Transition for Benzene
4.32: Modeling the Pi-electrons of Benzene as Particles in a Ring
4.33: Modeling the Pi-electrons of Corannulene as Particles in a Ring
4.34: The Vibrational and Electronic States of C60
05: Diffraction Phenomena
5.01: Using Optical Transforms to Teach Quantum Mechanics
5.02: Single-slit Diffraction and the Uncertainty Principle
5.03: Single-slit Diffraction and the Uncertainty Principle (Mathcad Version)
5.04: Simulating DNA's Diffraction Pattern
5.05: Simulating DNA's Diffraction Pattern with a More Realistic Model
5.06: Simulating DNA's Diffraction Pattern - Short Version
5.07: A Model Graphene Diffraction Pattern
5.08: Is a Two-dimensional Fibonacci Array a Quasilattice
5.09: Calculating Diffraction Patterns
5.10: Modeling the C60 Diffraction Pattern
5.11: Diffraction Pattern for Pentagonal Point Scatterers
5.12: Diffraction Pattern for Pentagonal Finite Point Scatterers
5.13: Pentagram Diffraction Pattern
5.14: Model Diffraction Pattern for Napthalene
5.15: Calculating the Airy Diffraction Pattern
5.16: Diffraction Pattern for Two Concentric Rings
5.17: Density Operator Approach to the Double-Slit Experiment
5.18: Another Look at the Double-Slit Experiment
5.19: A Quantum Mechanical Interpretation of Diffraction
5.20: Electron Diffraction at Multiple Slits
5.21: Multiple Slit Diffraction and the Fourier Transform
5.22: The Double-Slit Experiment with C60 Molecules
5.23: Crystal Structure Rotational Symmetry and Quasicrystals
5.24: X-ray Crystallography from a Quantum Mechanical Perspective
5.25: Holography Involves Single Photon Interference
5.26: X-ray Diffraction
5.27: Holography Involves Single Photon Interference
06: Group Theory with Mathcad
6.01: Group Theory Principles Applied to H2O
6.02: Dodecahedrane
6.03: Xenon Tetrafluoride
6.04: Diborane
6.05: Cubane
6.5.01: Buckminsterfulerene
6.06: BCl3
6.07: Ti(H2O)6 3
6.08: CH
6.09: P
6.10: Tetrahedrane
6.11: PH3
6.12: Cyclopropane
6.13: An Extensive Set of Group Theory Problems for Chemists
07: Quantum Optics
7.01: Single-Photon Interference - First Version
7.02: Single-Photon Interference - Second Version
7.03: Single-photon Interference - Third Version
7.04: Single Photon Interference - Fourth Version
7.05: Single Photon Interference - Mathcad version
7.06: The Polarizing Beam Splitter and the Superposition Principle
7.07: Mach-Zehner Polarization Interferometer Analyzed Using Tensor Algebra
7.08: Illustrating the Superposition Principle with Single Photon Interference
7.09: Pure States Mixtures and the Density Operator
7.10: Using the Trace Function to Calculate Expectation Values
7.11: Polarized Light and Quantum Superposition
7.12: Polarized Light and Quantum Mechanics
7.13: The Three-Polarizer Paradox
7.14: Matrix Mechanics Approach to Polarized Light
7.15: Matrix Mechanics Approach to Polarized Light - Version 2
7.16: Matrix Mechanics Exercises Using Polarized Light
7.17: Polarized Light and Quantum Mechanics
7.18: Neutron Interferometry with Polarized Spin States
7.19: Interaction Free Measurement - Seeing in the Dark
7.20: Quantum Seeing in the Dark - A Matrix-Tensor Analysis
7.21: Two Analyses of the Michelson Interferometer
7.22: A Quantum Circuit for a Michelson Interferometer
7.23: The Ramsey Atomic Interferometer
7.24: Optical Activity - A Quantum Perspective
7.25: A Quantum Optical Cheshire Cat
7.26: Two Photon Interference - The Creation of an Entangled Superposition
7.27: Two-particle Interference for Bosons and Fermions
7.28: Analysis of a Two-photon Interferometer
7.29: Two-photon Interferometry
7.29.01: Another Two Photon Interference Experiment
7.30: Another Two Photon Interference Experiment
7.31: Quantum Correlations Illuminated with Tensor Algebra
7.32: Two Photon Entanglement - A Tensor Algebra Analysis
7.33: Two Photon Interference - Matrix Mechanics Approach
7.34: Two-electron Interference
7.35: Bosonic and Fermionic Photon Behavior at Beam Splitters
7.36: Bosonic and Fermionic Photon Behavior at Beam Splitters- A Tensor Algebra Analysis
7.37: Entangled Photons Can Behave Like Fermions
7.38: Analyzing Two-photon Interferometry Using Mathcad and Tensor Algebra
7.39: Analysis of a Two-photon Quantum Eraser
7.40: Another Example of a Two-photon Quantum Eraser
7.41: A Quantum Delayed-Choice Experiment
7.42: A Quantum Delayed-Choice Experiment
08: Quantum Teleportation
8.01: A Single Page Summary of Quantum Teleportation
8.02: Quantum Teleportation - A Brief Introduction
8.03: Quantum Teleportation at a Glance
8.04: Another Look at Quantum Teleportation
8.05: Teleportation Using Quantum Gates
8.06: Another Example of Teleportation Using Quantum Gates
8.07: Yet Another Quantum Teleportation Circuit
8.08: Quantum Teleportation - Another Look
8.09: A Quantum Teleportation Experiment for Undergraduates
8.10: A Simple Teleportation Exercise
8.11: Teleportation as a Quantum Computation
8.12: Quantum Teleportation - Four Perspectives
8.13: Teleportation of Two Qubits
8.14: Greenaberger-Hrne-Zeilinger (GHZ) Entanglement and Local Realism
8.15: GHZ Math Appendix
8.16: GHZ Entanglement - A Tensor Algebra Analysis
8.17: Simulation of a GHZ Gedanken Experiment
8.18: Another Simulation of a GHZ Gedanken Experiment
8.19: A Surgical Refutation of the Local Realism Heresy
8.20: GHZ Four-Photon Entanglement Analyzed Using Tensor Algebra
8.21: Quantum v. Realism
8.22: Elements of Reality- Another GHZ Gedanken Experiment Analyzed
8.23: Brief Elements of Reality
8.24: A Brief Analysis of Mermin's GHZ Thought Experiment
8.25: Lucien Hardy's Paradox as Presented by N. David Mermin
8.26: Hardy's Paradox - An Algebraic Analysis
8.27: Quantum Entanglement Leads to Nonclassical Correlations
8.28: Nonclassial Correlations Revealed with Mermin's Pentagram
8.29: Spooky Action at a Distance- The EPR Experiment with Photons
8.30: David Bohm's EPR Gedanken Experiment
8.31: An Extension of Bohm's EPR Experiment
8.32: A Surgical Adjudication of the Conflict Between Quantum Theory and Local Realism
8.33: A Thought Experiment Reveals the Conflict Between Quantum Theory and Local Realism
8.34: Positronium Annihilation
8.35: Mermin's Version of Bohm's EPR Gedanken Experiment
8.36: A Concise Version of Mermin's EPR Gedanken Experiment
8.37: Another Look at Mermin's EPR Gedanken Experiment
8.38: Mermin's Version of Bohm's EPR Gedanken Experiment Using Tensor Algebra
8.39: A GHZ Gedanken Experiment Using Spatial Degrees of Freedom and Tensor Algebra
8.40: Another GHZ Example Using Spin-1 2 Particles
8.41: Entanglement Reveals a Conflict Between Local Realism and Quantum Theory
8.42: A Summary of Feynman's Simulating Physics with Computers
8.43: Another Summary of Fenyman's Stimulating Physics with Computers
8.44: Yet Another Assault on Local Realism
8.45: Yet Another Assault on Local Realism - A Matrix Tensor Algebra Approach
8.46: Jim Baggott's Bell Theorem Analysis
8.47: Another Bell Theorem Analysis
8.48: Another Bell Theorem Analysis - Shorter Version
8.49: EPR Analysis for a Composite Singlet Spin System
8.50: EPR Analysis for a Composite Singlet Spin System - Short Version
8.51: Analysis of the Stern-Gerlach Experiment
8.52: Hardy's Paradox
8.53: Bell State Exercises
8.54: Expressing Bell and GHZ States in Vector Format Using Mathcad
8.55: Quantum Circuit for the Generation of GHZ States
8.56: A Brief Description of Aspect's Experiment
8.57: The Kochen-Specker Theorem Illustrated Using a Three-Qubit GHZ System
8.58: A Brief Introduction to Entanglement Swapping
8.59: An Entanglement Swapping Protocol
8.60: Quantum Correlations Simplified
8.61: Simulating Quantum Correlations with a Quantum Computer
8.62: Quantum Computer Simulation of Photon Correlations
8.63: Quantum Correlations Illustrated with Photons
8.64: Examining the Local States of an Entangled Bipartate Superposition
8.65: A Brief Introduction to the Quantum Computer
8.66: A Very Simple Example of Parallel Quantum Computation
8.67: Another Simple Example of Parallel Quantum Computation
8.68: A Simple Solution to Deutsch's Problem
8.69: Another Example of Deutsch's Algorithm
8.70: Evaluating a Function Using a Quantum Circuit and a Demonstration of Parallel Computation
8.71: A Simple Quantum Circuit for Parallel Computation
8.72: An Illustration of the Deutsch-Jozsa Algorithm
8.73: Another Illustration of the Deutsch-Jozsa Algorithm
8.74: Aspects of Simon's Algorithm
8.75: Qubit Quantum Mechanics
8.76: Implementation of Deutsch's Algorithm Using Mathcad
8.77: Using Quantum Gates to Create Superpositions and Entangled States
8.78: A Simple Quantum Computer
8.79: Solving Equations Using a Quantum Circuit
8.80: Introduction to Superdense Coding
8.81: A Brief Introduction to Quantum Dense Coding
8.82: The Discrete or Quantum Fourier Transform
8.83: Factoring Using Shor's Quantum Algorithm
8.84: Shor's Quantum Algorithm - A Summary
8.85: Simulating the Deutsch-Jozsa Algorithm with a Double-Slit Apparatus
8.86: Simulating a Quantum Computer with a Mach-Zehnder Interferometer
8.87: Quantum Restrictions on Cloning
8.88: Quantum Error Correction
8.89: Matrix Mechanics Analysis of the BB84 Key Distribution
8.90: 388. The Quantum Math Behind Ekert's Key Distribution Scheme
8.91: A Shorter Version of the Quantum Math Behind Ekert's Key Distribution Scheme
8.92: Quantum Key Distribution Using a Mach-Zehnder Interferometer
8.93: Coding and Decoding Venus
8.94: Grover's Quantum Search Algorithm
8.95: Grover's Search Algorithm- Implementation for Two Items
8.96: Grover's Search Algorithm- Four-Card Monte
09: Numerical Solutions for Schrodinger's Equation
9.01: Introduction to Numerical Solutions of Schodinger's Equation
9.02: Particle in an Infinite Potential Well
9.03: Particle in a Gravitational Field
9.04: Particle in a One-dimensional Egg Carton
9.05: Particle in a Finite Potential Well
9.06: Particle in a Semi-infinite Potential Well
9.07: Particle in a Slanted Well Potential
9.08: Numerical Solutions for a Particle in a V-Shaped Potential Well
9.09: Numerical Solutions for the Harmonic Oscillator
9.10: Numerical Solutions for a Double-Minimum Potential Well
9.11: Numerical Solutions for the Quartic Oscillator
9.12: Numerical Solutions for Morse Oscillator
9.13: Numerical Solutions for the Lennard-Jones Potential
9.14: Numerical Solutions for the Double Morse Potential
9.15: Particle in a Box with an Internal Barrier
9.16: Another Look at the in a Box with an Internal Barrier
9.17: Particle in a Box with Multiple Internal Barriers
9.18: Particle in an Infinite Spherical Potential Well
9.19: Numerical Solutions for the Two-Dimensional Harmonic Oscillator
9.20: Numerical Solutions for the Three-Dimensional Harmonic Oscillator
9.21: Numerical Solutions for the Hydrogen Atom Radial Equation
9.22: Numerical Solutions for a Modified Harmonic Potential
10: Approximate Quantum Mechanical Methods
10.01: Trial Wavefunctions for Various Potentials
10.02: Energy Minimization - Four Methods Using Mathcad
10.03: The Variation Theorem in Dirac Notation
10.04: A Rudimentary Model for Alpha Particle Decay
10.05: Variational Method for a Particle in a Finite Potential Well
10.06: Variation Method for a Particle in a Symmetric 1D Potential Well
10.07: Variation Method for the Rydberg Potential
10.08: Variation Method for the Quartic Oscillator
10.09: Momentum-Space Variation Method for the Quartic Oscillator
10.10: Variation Method for a Particle in a Gravitational Field
10.11: Linear Variational Method for a Particle in a Slanted 1D Box
10.12: Variation Method for a Particle in a Semi-Infinite Potential Well
10.13: Variation Method for a Particle in a Box with an Internal Barrier
10.14: Variation Method for a Particle in a 1D Ice Cream Cone
10.15: Variation Method for a Particle in an Ice Cream Cone
10.16: Variation Method for a Particle in a Finite 3D Spherical Potential Well
10.17: Variation Method for the Harmonic Oscillator
10.18: Trigonometric Trial Wave Function for the Harmonic Potential Well
10.19: Trigonometric Trial Wave Function for the 3D Harmonic Potential Well
10.20: Gaussian Trial Wavefunction for the Hydrogen Atom
10.21: Variation Calculation on the 1D Hydrogen Atom Using a Trigonometric Trial Wave Function
10.22: Variation Calculation on the 1D Hydrogen Atom Using a Gaussian Trial Wavefunction
10.23: Variational Calculation on the Two-dimensional Hydrogen Atom
10.24: Variational Calculation on Helium Using a Hydrogenic Wavefunction
10.25: Gaussian Trial Wave Function for the Helium Atom
10.26: Trigonometric Trial Wavefunction for the Helium Atom
10.27: Trigonometric Trial Wavefunction for the Hydrogen Atom
10.28: Hydrogen Atom Calculation Assuming the Electron is a Particle in a Sphere of Radius R
10.29: Electronic Structure - Variational Calculations on the Lithium Atom
10.30: The Variation Method in Momentum Space
10.31: Momentum-Space Variation Method for Particle in a Gravitational Field
10.32: Momentum-Space Variation Method for the Abs(x) Potential
10.33: Variational Method for the Feshbach Potential
10.34: Numerical Solution for the Feshbach Potential
10.35: First Order Degenerate Perturbation Theory - the Stark Effect of the Hydrogen Atom
10.36: Variational Calculation for the Polarizability of the Hydrogen Atom
10.37: Hybrid Variational Calculation for the 1D Hydrogen Atom with Delta Function Potential
10.38: Variation Method Using the Wigner Function- Finite Potential Well
10.39: 455. Variation Method Using the Wigner Function- V(x) x
10.40: Variation Method Using the Wigner Function- The Harmonic Oscillator
10.41: Variation Method Using the Wigner Function - The Quartic Oscillator
10.42: Variation Method Using the Wigner Function - The Feshbach Potential
11: Miscellaneous
11.01: The Art of Science
11.02: Mass-Energy Equivalence
11.03: Commentary on Probing the Orbital Energy of an Electron in an Atom
11.04: The Use of Models in Introductory Chemistry
11.05: Reaction to Gillespie's Six Great Ideas in Chemistry - Another Great Idea
11.06: An Alternative Derivation of Gas Pressure Using the Kinetic Theory
11.07: Examining Fourier Synthesis with Dirac Notation
11.08: Finding Roots of Transcendental Equations
11.09: Calculation of the Composition of a Weak Polyprotic Acid Using Mathcad
11.10: Solving Linear Equations Using Mathcad
11.11: Let's Teach High School Students Computer Algebra Methods
11.12: Thermodynamics and Kinetics
11.13: Simple Kinetic Derivations of Thermodynamic Relations
11.14: The Global Approach to Thermodynamics
11.15: Global Thermodynamic Analyses of Heat Engines
11.16: Using Charles' Law to Determine Absolute Zero
11.17: The Origin of KE 3 2 RT
11.18: Cosmic Background Radiation
11.19: Age of the Elements