- A Lattice Energy Calculation for LiH Lithium hydride is a white crystalline solid with the face-centered cubic crystal structure. The model for LiH(s)
- Density Operator Approach to the Double-Slit Experiment Frank Rioux
- AB Proton NMR Using Tensor Algebra Frank Rioux
- Vol. 74 No. 5 May 1997 Journal of Chemical Education 605 Information Textbooks Media Resources
- Demonstrating the Uncertainty Prinicple for Angular Momentum and Angular Position
- Lucien Hardy's Paradox as Presented by N. David Mermin Frank Rioux
- Bosonic and Fermionic Behavior at Beam Splitters Analyzed Using Tensor Algebra
- Calculating the Atomic Radius of Polonium Frank Rioux
- Two Perspectives on the Bonding in Water Frank Rioux
- Elements of Reality Frank Rioux
- 12 Chem. Educator 2004, 9, 1216 Using Optical Transforms To Teach Quantum Mechanics
- Two-Particle Interference for Bosons and Fermions A parametric down converter, PDC, transforms an incident photon into two lower energy
- A Quantum Mechanical Interpretation of Singleslit Diffraction Or, Using Diffration Phenomena to Illustrate the Uncertainty Principle
- What Does Huckel MOT Have to Say About the Stability of the C10H8 Isomers? Frank Rioux
- Quantum Entanglement Leads to Nonclassical Correlations Frank Rioux
- 1 / V O L . 2 , N O . 6 I S S N 1 4 3 0 -4 1 7 1 T H E C H E M I C A L E D U C A T O R h t t p : / / j o u r n a l s . s p r i n g e r -n y . c o m / c h e d r
- A Charge Cloud Model for H2: Or Is It a DFT Model? Frank Rioux
- Visualizing the Difference Between a Superposition and a Mixture Frank Rioux
- Chemical Education Today 1404 Journal of Chemical Education Vol. 79 No. 12 December 2002 JChemEd.chem.wisc.edu
- exp i-p x1( ) exp i-p x2( )+
- Momentum Operator in Coordinate Space Wave-particle duality is at the heart of quantum mechanics. A particle with wavelength 8 has
- 288 Chem. Educator 2001, 6, 288290 The Covalent Bond in H2
- Analysis of a Temporal Double-slit Experiment Frank Rioux
- Simple Variational Calculations on Multi-electron Atoms and Ions Frank Rioux
- RUSSELLH. BAT^ KenyonCollege
- Modeling Cyanine Dyes as Two-state Electronic Systems Frank Rioux
- AB Proton NMR Analysis for 2,3dibromothiophene Frank Rioux
- Pure States, Mixtures and the Density Operator Frank Rioux
- 0 2 4 6 8 10 12 14 2pz r 0,( )
- Harmonic Potential with Gaussian Barrier Model for Ammonia Inversion Frank Rioux
- Simulating the Aharonov-Bohm Effect Frank Rioux
- Electronic Spectrum of a Transition Metal Complex This exercise has to do with the interpretation of the visible spectrum Ti(H20)63+ which is shown below.
- Molecular Structures for Azatitanatranes Frank Rioux, Michael W. Schmidt, and Mark S. Gordon*
- Matrix Mechanics Approach to Polarized Light Frank Rioux
- Variational Calculations on the Lithium Atom The electronic structure of lithium is 1s22s1. The hydrogenic 1s and 2s orbitals are as follows
- X-ray Diffraction: A Quantum Mechanical View Frank Rioux
- Quantum Entanglement Leads to Nonclassical Correlations Frank Rioux
- The Temporal Double-Slit Experiment Frank Rioux
- Crystal Structure and Rotational Symmetry Frank Rioux
- Numerical Solutions for a Modified Harmonic Potential Frank Rioux
- Localized and Delocalized Wave Functions for Butadiene Frank Rioux
- A Really Simple SCF Calculation Selfconsistent field calculations have great historical significance and play a major role in
- Kinetic Energy Is Important in the Nanoscale World Frank Rioux
- The DoubleSlit Experiment with Polarized Light Frank Rioux
- The Quantum Jump Another Look Frank Rioux
- A Comment on the Vibrational Analysis for C60 and Other Fullerenes Frank Rioux
- Mach-Zehnder Polarizing Interferometer Analyzed Using Tensor Algebra
- The global approach to thermodynamics: Try it, you'll like it Frank Rioux
- A de Broglie-Bohr Model for the Hydrogen Atom Frank Rioux
- Variational Calculation on the Helium Atom Using a Trigonometric Trial Wave Function Frank Rioux
- The 1s-2s Electronic Transition in the 1D Hydrogen Atom Frank Rioux
- Visualizing the Formally Forbidden Overtone Vibrational Transitions in HCl Using the harmonic oscillator model, the selection rule for molcecular vibrations is v = +/-1. However, overtone
- Trigonimetric Trial Wave Function for the Hydrogen Atom Trial wave function: r ,( ) 3
- Another Attack on Local Realism Frank Rioux
- C3v Symmetry -PH3 (pyramidal) has IR and Raman active vibrations at 2421, 2327, 1121, and 991 cm-1. Make assignments in terms of
- Covalent Bonding in Ammonia from Several Perspectives Frank Rioux
- GreenbergerHorneZeilinger (GHZ) Entanglement and Local Realism Analyzed Using Tensor Algebra
- Numeric Huckel Molecular Orbital Calculations for Anthracene and Phenanthrene Frank Rioux
- Chem. Educator 2003, 8, 13 (web)1 The Covalent Bond Examined Using the Virial Theorem
- Spliting the 2s-2p Degeneracy in Lithium Frank Rioux
- INSTITUTE OF PHYSICS PUBLISHING EUROPEAN JOURNAL OF PHYSICS Eur. J. Phys. 24 (2003) N1N3 PII: S0143-0807(03)58246-0
- C60 Has Icosahedral Symmetry Buckminsterfullerene has four IR active vibrational modes (528, 577, 1180, 1430 cm-1) and ten Raman acitve modes
- Chemical Education Today 706 Journal of Chemical Education Vol. 77 No. 6 June 2000 JChemEd.chem.wisc.edu
- Chemical Education Today 156 Journal of Chemical Education Vol. 76 No. 2 February 1999 JChemEd.chem.wisc.edu
- SCF Calculation for Two Electron Atoms and Ions Using a Gaussian Wave Function
- A Mechanistic Approach to Bond Formation in H2 Frank Rioux
- Chemical Education Today JChemEd.chem.wisc.edu Vol. 76 No. 5 May 1999 Journal of Chemical Education 605
- The Difference Between Fermions and Bosons n 1 1 n 2 2 ( )x .2 sin ..n 1 x ( )x .2 sin ..n 2 x
- An Approach to Quantum Mechanics Frank Rioux
- Another Look at the Wigner Function Frank Rioux
- How Many Bibles Can Fit on the Head of a Pin Frank Rioux
- Analysis of the Stern-Gerlach Experiment Frank Rioux
- Creating Superpositions and Entangled States Using Quantum Gates Frank Rioux
- Vol. 74 No. 8 August 1997 Journal of Chemical Education 1015 Information Textbooks Media Resources
- DoubleSlit Experiment with Polarized Light Frank Rioux
- Another GHZ Example Using Spin-1/2 Particles Frank Rioux
- Roothaan's Method in One-Dimension Donald K. Harriss
- Numerical Solutions for the Infinite Potential Well with Internal Barrier The purpose of this tutorial is to explore the impact of the presence of a large (100 Eh) thin (0.10 a0) internal barrier on the
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- Chem. Educator 2007, 12, 243245 243 Bohr Model Calculations for Atoms and Ions
- An Alternative Derivation of Gas Pressure Using the Kinetic Theory Frank Rioux
- Bosonic and Fermionic Photon Behavior at Beam Splitters Frank Rioux
- Simulating the DNA Diffraction Pattern Frank Rioux
- Information Textbooks Media Resources 644 Journal of Chemical Education Vol. 75 No. 5 May 1998 JChemEd.chem.wisc.edu
- Finding Roots The attempt to find analytical solutions to Schrodingers equation for some problems yields
- Chemists are concerned with molecules; their archi-tecture, physical properties, and the physical and chemi-
- Electronic Spectrum of a Transition Metal Complex Frank Rioux
- Physical Nature of the Covalent Bond This study of the nature of the H2
- The Art of Science Frank Rioux
- Teleportation Using Quantum Gates Frank Rioux
- A Rudimentary Analysis of the VibrationalRotational HCl Spectrum Frank Rioux
- In the Classroom 1210 Journal of Chemical Education Vol. 82 No. 8 August 2005 www.JCE.DivCHED.org
- Chemical Education Today JChemEd.chem.wisc.edu Vol. 75 No. 5 May 1998 Journal of Chemical Education 537
- Atomic Spectroscopy Planck's constant: h 6.62608 10
- Tetrahedral Symmetry for Methane The infrared spectrum of methane shows two absorptions: a bend at 1306 cm-1 and a stretch at 3019 cm-1. Demonstrate that a
- Another Great Idea Frank Rioux
- Superposition vs. Mixture Frank Rioux
- Hydrogen Atom and Helium Ion Spatial and Momentum Distribution Functions Illustrate the Uncertainty Principle
- An Interactive SCF Calculation Frank Rioux
- Absorption Spectra of ColorCenters Frank Rioux
- A Molecular Orbital Approach to Bonding in Methane Frank Rioux
- Analyzing Two-Photon Interferometry Using Mathcad and Tensor Algebra Frank Rioux
- Diborane -D2h Symmetry Diborane has 18 vibrational degrees of freedom. Nine modes are Raman active and eight are IR active. The experimental
- Quantum Dynamics: One Step at a Time Frank Rioux
- AB Proton NMR Using Tensor Algebra Frank Rioux
- The Quantum Eraser Frank Rioux
- Group Theoretical Analysis of the Vibrational and Electronic Spectrum of Benzene Frank Rioux
- The Virial Theorem and the Covalent Bond in H2 Frank Rioux
- The Chemical Bond and Quantum Mechanics* The behavior of electrons in molecules and atoms is described by
- Tangent Spheres Critique of VSEPR for CH4 This analysis uses Henry Bents Valence Spheres Model (VSM) to analyse the VSEPR claim that the
- Frank Rioux St. John's University
- Five Trial Wavefunctions for two-electron Atoms and Ions The purpose of this exercise is to examine five trial wavefunctions for the helium atom and several
- Variational Calculation on the Simple Harmonic Oscillator in Momentum Space The following normalized trial wave function is proposed for a variational calculation on the
- Ithas been noted frequentlythat it is very difficult forun-dergraduates to come to grips with the fundamentals of
- The Hyperfine Splitting in the Hydrogen Atom Frank Rioux
- Chem. Educator 2003, 8, 237237 237 An Alternative Derivation of Gas Pressure Using the Kinetic Theory
- The Kinetic Molecular Theory of Gases A gas consists of a collection of molecules in continuous random motion with
- Mermin's Version of Bohm's EPR Gedanken Experiment Frank Rioux
- Fifth Trial Wavefunction exp -r1( ) exp -r2( ) exp -r1( ) exp -r2( )+( ) 1 b r12+( )=
- Commentary on "Probing the Orbital Energy of an Electron in an Atom"
- The Hydrogen Atom with a Finite Sized Nucleus Frank Rioux
- Td -Tetrahedral Symmetry for P4 The following Raman and IR frequencies have been observed for the tetrahedral P4 molecule. Is the assignment of
- Trial Wave Function for Particle in Slanted Box Trial wave functions: 1 x( ) 2 sin x( ):= 2 x( ) 105 x 1 x-( )
- Quantum Tunneling in Coordinate, Momentum and Phase Space Frank Rioux
- Calculations on the One-dimensional H-Atom in Coordinate and Momentum Space
- Symmetry Analysis for Cubane Cubane, C8H8, has 42 vibrational degrees of freedom, but only three IR active modes. Cubane belongs to the
- Illustrating the Superposition Principle with Single Photon Interference Frank Rioux
- Research: Science and Education 358 Journal of Chemical Education Vol. 84 No. 2 February 2007 www.JCE.DivCHED.org
- 424 Chem. Educator 2005, 10, 424426 Illustrating the Superposition Principle with Single-Photon Interference
- Chem. Educator 2004, 9, 15 (web)1 2004 The Chemical Educator, S1430-4171(04)0xxxx-x, Published on Web xx/xx/2003, 10.1333/s00897040611a, xxxxxxaa.pdf
- 200 Chem. Educator 2002, 7, 200204 Polarized Light and Quantum Mechanics: An Optical Analog of the
- Chemical Education Today JChemEd.chem.wisc.edu Vol. 79 No. 1 January 2002 Journal of Chemical Education 29
- NOTES AND DISCUSSIONS KronigPenney model with the tail-cancellation method
- the computer bulletin"board
- St.John's University I cCollegeville,Minnesota 56321
- Quantum Mechanics and the Fourier Transform Frank Rioux
- Exploring the Origin of Schrdinger's Equations Frank Rioux
- Basic Quantum Mechanics in Coordinate, Momentum and Phase Space
- The Repackaging of Quantum Weirdness Frank Rioux
- Quantum Principles Illuminated with Polarized Light Frank Rioux
- Elements of Dirac Notation Frank Rioux
- The Dirac Notation Applied to Variational Calculations The particle-in-a-box problem is exactly soluble and the solution is calculated below for the first 20 eigenstates.
- Raising & Lowering; Creating & Annihilating Frank Rioux
- The Position and Momentum Commutation Relation in Coordinate and Momentum Space
- Matrix Mechanics Frank Rioux
- An Analysis of ThreePath Interference Frank Rioux
- Using a Mach-Zehnder Interferometer to Illustrate Feynman's Sum Over Histories Approach to Quantum Mechanics
- Quantized Gravitational States A Variational Approach
- Energy Expectation Values and the Origin of the Variation Principle A system is in the state , which is not an eigenfunction of the energy operator, . A
- Wigner Distribution for the Double Slit Experiment Illumination of a double slit with a coherent incident particle beam leads to a "cat state" which can be represented by
- Wigner Distribution for the Particle in a Box The Wigner function is a quantum mechanical phase-space quasi-probability function. It is called a
- A Graphical Illustration of the Heisenberg Uncertainty Relationship Frank Rioux
- The Harmonic Oscillator and the Uncertainty Principle Schroedinger's equation in atomic units (h = 2) for the harmonic oscillator has an exact analytical
- The PositionMomentum Uncertainty Relation in the Hydrogen Atom
- Quantum Corrals: Electrons in a Ring Frank Rioux
- Wave-particle Duality and the Uncertainty Principle Nick Herbert, author of Quantum Reality, has proposed the name quon for "any entity that exhibits both wave
- Quantum Mechanical Pressure Frank Rioux
- Analysis of the Stern-Gerlach Experiment Using Matirx Mechanics Frank Rioux
- The de Broglie-Bohr Model for the Hydrogen Atom = de Broglie's hypothesis that
- The deBroglie-Bohr Model for the Hydrogen Atom = de Broglie's hypothesis that
- The deBroglie-Bohr Model for a Hydrogen Atom Held Together by a Gravitational Interaction = de Broglie's hypothesis that
- Atomic Spectroscopy and the Correspondence Principle Frank Rioux
- Exploring the Role of Lepton Mass in the Hydrogen Atom Frank Rioux
- The Hyperfine Splitting in the Deuterium Atom Frank Rioux
- Why Isn't the Ground State Electronic Structure of the Lithium Atom 1s3? The purpose of this tutorial is to point out that if all that mattered in the determination of atomic structure was
- Two-parameter Study of the 1s2s Excited State of He and Li+ -Hund's Rule The trial variational wave functions for the 1s1
- Quantum Chemistry Computer Laboratory VII Approximate Methods: Variational Calculations for Two-electron Species
- Second Trial Wavefunction exp -r1( ) exp -r2( ) exp -r1( ) exp -r2( )+ exp -r1( ) exp -r2( )+ exp -r1( ) exp -r2( )+=
- Third Trial Wavefunction exp -r1( ) exp -r2( ) exp -r1( ) exp -r2( )+=
- Fourth Trial Wavefunction r( ) exp -r1 r2+( ) 1 r12+( )=
- A Mechanistic Approach to Bond Formation in H2 Frank Rioux
- A Onedimensional Model for the Covalent Bond in H2 Frank Rioux
- A Lattice Energy Calculation for LiH Frank Rioux
- A Simple Electrostatic Critique of VSEPR Frank Rioux
- Tangent Spheres Model (TSM) Calculation for Trigonal Bipyramid Electron Pair Geometry Frank Rioux
- A Modified Tangent Spheres Model (TSM) Calculation for Trigonal Bipyramid Electron Pair Geometry
- Huckel Molecular Orbital Theory for Buckminsterfullerene 1. Number the carbons after inspection of the molecular structure and fill in data needed below.
- Chemical Bonding and Electronic Structure of Buckminsterfullerene As is well-known C60 resembles an American soccerball, containing 12 pentagons and
- Quantum Mechanics, Group Theory, and C60 Frank Rioux
- Semi-emprical Molecular Orbital Calculation on HF Calculate the wavefunctions and energies of the orbitals in the HF molecule, taking = -1.0 eV. The values
- Semi-emprical Molecular Orbital Calculation on XeF2 The bonding in XeF2 can be interpreted in terms the three-center four-electron bond. In linear XeF2 the molecular
- Analyses of the Pure Rotational Spectrum of HCl Frank Rioux
- Quantum Jumps for an Electron in a One-dimensional Box The phrases "quantum jump" and "quantum leap" are used in everyday discourse. This disguises
- Quantum Beats Frank Rioux
- Quantum Jumps for an Electron on a Ring Frank Rioux
- ABC Proton NMR Using Tensor Algebra Frank Rioux
- The Michelson Interferometer and Fourier Transform Spectroscopy A Michelson interferometer with a movable mirror in one arm is an essential element in Fourier Transform (FT)
- Modeling the -lectrons of Benzene as Particles on a Ring Calculate the wavelength of the photon required for the first allowed (HOMO-LUMO) electronic
- Vibrational and Electronic States of C60 Frank Rioux
- Is a Two-dimensional Fibonacci Array a Quasilattice? Frank Rioux
- Calculating Diffraction Patterns Frank Rioux
- Calculating the Airy Diffraction Pattern Frank Rioux
- A Quantum Mechanical Interpretation of Single-slit Diffraction Or, Using Diffration Phenomena to Illustrate the Uncertainty Principle
- X-ray Crystallography from a Quantum Mechanical Perspective Frank Rioux
- Group Theory for Dodecahedrane When Paquette's group synthesized dodecahedrane, C20H20, they measured its infrared and Raman spectra (JACS 1983,
- Symmetry, Spectroscopy, and the Molecular Structure of XeF4 The infrared spectrum of XeF4 has absorptions at 161, 291, and 586 cm-1 (two bends, one stretch), while the Raman
- C3v Symmetry -BCl3 The infrared spectrum of BCl3 shows vibrational bands at 995, 480, and 244 cm-1, while Raman bands appear at 995,
- Symmetry Analysis for Tetrahedrane Tetrahedrane, C4H4, belongs to the Td point group. Use group theory to predict the number of IR and Raman
- D3h Symmetry -C3H6 The following IR and Raman spectroscopic data is available for cyclopropane, C3H6. Demonstrate that this data is consistent
- Group Theory Problems The following table shows the vibrational frequencies of CH4. Assuming CH4 belongs to the Td point group, fill in
- Using Dirac Notation to Analyze Single Particle Interference Frank Rioux
- Polarized Light and the Quantum Superposition Frank Rioux
- Polarized Light and Quantum Mechanics Introduction
- Matrix Mechanics Approach to Polarized Light Frank Rioux
- Matrix Mechanics Exercises Using Polarized Light Frank Rioux
- Neutron Interferometry with Polarized Spin States Frank Rioux
- Interaction Free Measurement: Seeing in the Dark Frank Rioux
- Analysis of a Twophoton Interferometer Frank Rioux
- Two-photon Interference: A Matrix Mechanics Approach prepared by
- Twoelectron Interference Frank Rioux
- Bosonic and Fermionic Photon Behavior at Beam Splitters Analyzed Using Tensor Algebra
- Quantum Teleportation: A Brief Outline Frank Rioux
- Quantum Teleportation at a Glance Frank Rioux
- Quantum Teleportation Examined with Tensor Algebra Frank Rioux
- GHZ Appendix This appendix show another way of "doing the math" in the GHZ experiment.
- GHZ Four-Photon Entanglement Analyzed Using Tensor Algebra Frank Rioux
- A GHZ Example Using Spatial Degrees of Freedom and Tensor Algebra Frank Rioux
- Entanglement Reveals a Conflict Between Local Realism and Quantum Theory Frank Rioux
- Another Assault on Local Realism Frank Rioux
- Hardy's Paradox Frank Rioux
- Matrix Math for Qubit Quantum Mechanics... by Enrique Galvez, AJP 78, 510-519 (2010) Prepared by Frank Rioux
- Implementation of Deutsch's Algorithm Using Mathcad Frank Rioux
- Solving Schrodinger's Equation Numerically Using Mathcad Solving Schrodinger's equation is the primary task of chemists in the field of quantum chemistry. However, exact solutions for
- Numerical Solutions for Schrodinger's Equation Particle in a Box with an Internal Barrier
- A Rudimentary Model for Alpha Decay Frank Rioux
- Approximate Methods: The Quartic Oscillartor For unit mass the quartic oscillator has the following energy operator in atomic units.
- Variational Approach to the Harmonic Oscillator This exercise deals with a variational treatment for the ground state of the simple harmonic
- Variation Method Calculation on a One-dimensional Model for the Hydrogen Atom Using a Trigonometric Trial Wavefunction
- Variation Method Calculation on a One-dimensional Model for the Hydrogen Atom Using a Gaussian Trial Wavefunction
- Variational Calculation on the Helium Atom Using a Hydrogenic Trial Wave Function Frank Rioux
- Approximate Methods: The Quartic Oscillartor in Momentum Space For unit mass the quartic oscillator has the following energy operator in atomic units in coordinate space.
- First Order Degenerate Perturbation Theory The Stark Effect for the Hydrogen Atom
- Variational Calculation for the Polarizability of the Hydrogen Atom Frank Rioux
- Teach High School Students Computer Algebra Methods Frank Rioux
- Global Thermodynamic Analysis of Heat Engines Frank Rioux
- Using Charles' Law to Determine Absolute Zero A simple experiment to determine absolute zero using Charles' Law is illustrated below. An erlenmeyer
- Frank Rioux Saint John's University, Collegeville,MN 56321
- pH 2.188=pH log 6.49 10 The last row contains the physically meaningful solution to the fifth order polynomial that is solved. The pH of this solution
- Variation Method for a Particle in a Box with an Internal Barrier 1 x( ) 2 sin x( ):= 2 x( ) 2 sin 3 x( ):= V x( ) if x .45( ) x .55( ) 3, 0,[ ]:=
- Cosmic Background Radiation n 43:= i 1 n..:= The cosmic background radiation fills all space and is a relic from the "big bang"
- Chem. Educator 2004, 9, 353355 353 Kinetic Energy is Important in the Nanoscale World
- Bohr Model Calculations for Atoms and Ions Frank Rioux
- Examining the Wigner Distribution Using Dirac Notation Frank Rioux
- GreenbergerHorneZeilinger (GHZ) Entanglement and Local Realism Frank Rioux
- The Quantum Bouncer Doesnt Bounce, Unless... Frank Rioux
- The Harmonic Oscillator and the Uncertainty Principle In atomic units the wave function in coordinate space for an harmonic oscillator with reduced mass, ,
- The Onedimensional Hydrogen Atom with a Delta Function Potential Energy Interaction Between the Proton and Electron
- Variational Calculations on the Lithium Atom The electronic structure of lithium is 1s 22s1. The hydrogenic 1s and 2s orbitals are as follows
- Quantum Correlations Illuminated Using Tensor Algebra Frank Rioux
- Another Assault on Local Realism Frank Rioux
- Two Analyses of the Michelson Interferometer Frank Rioux
- A Brief Analysis of Mermin's GHZ Thought Experiment Frank Rioux
- HDLike NMR Spectrum Calculated Using Tensor Algebra Frank Rioux
- Quantum Seeing in the Dark Frank Rioux
- A Simple Quantum Computer Frank Rioux
- A SternGerlach Quantum Eraser Frank Rioux