Lec 8 - One-Dimensional Wave Functions

"Lec 8 - One-Dimensional Wave Functions" Freshman Organic Chemistry (CHEM 125) Professor McBride expands on the recently introduced concept of the wave function by illustrating the relationship of the magnitude of the curvature of the wave function to the kinetic energy of the system, as well as the relationship of the square of the wave function to the electron probability density. The requirement that the wave function not diverge in areas of negative kinetic energy leads to only certain energies being allowed, a property which is explored for the harmonic oscillator, Morse potential, and the Columbic potential. Consideration of the influence of mass reveals an "isotope effect" on dynamics, on the energy, vibration frequency, and length of bonds. 00:00 - Chapter 1. Review: The Curvature of the Wave Function and Kinetic Energy 06:44 - Chapter 2. Relationships between Nodes and Curvature of the Wave Function 23:49 - Chapter 3. The Square of Psi as the Probability Density 31:46 - Chapter 4. Constraints of Energy in the Harmonic Oscillator, the Morse Potential and the Coulombic Potential 42:12 - Chapter 5. The Influence of Mass on Bond Dynamics, Strength, and Distance Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses This course was recorded in Fall 2008.

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Channels: Chemistry (General)

Tags: Schrödinger equation wave function negative kinetic energy curvature nodes

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Duration: 49m 51s

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Lecture list for this course

Lec 1 - How Do You Know?

Lec 2 - Force Laws, Lewis Structures and Resonance

Lec 3 - Double Minima, Earnshaw's Theorem and Plum-Puddings

Lec 4 - Coping with Smallness and Scanning Probe Microscopy

Lec 5 - X-Ray Diffraction

Lec 6 - Seeing Bonds by Electron Difference Density

Lec 7 - Quantum Mechanical Kinetic Energy

Lec 9 - Chladni Figures and One-Electron Atoms

Lec 10 - Reality and the Orbital Approximation

Lec 11 - Orbital Correction and Plum-Pudding Molecules

Lec 12 - Overlap and Atom-Pair Bonds

Lec 13 - Overlap and Energy-Match

Lec 14 - Checking Hybridization Theory with XH_3

Lec 15 - Chemical Reactivity: SOMO, HOMO, and LUMO

Lec 16 - Recognizing Functional Groups

Lec 17 - Reaction Analogies and Carbonyl Reactivity

Lec 18 - Amide, Carboxylic Acid and Alkyl Lithium

Lec 19 - Oxygen and the Chemical Revolution (Beginning to 1789)

Lec 20 - Rise of the Atomic Theory (1790-1805)

Lec 21 - Berzelius to Liebig and Wöhler (1805-1832)

Lec 22 - Radical and Type Theories (1832-1850)

Lec 23 - Valence Theory and Constitutional Structure (1858)

Lec 24 - Determining Chemical Structure by Isomer Counting (1869)

Lec 25 - Models in 3D Space (1869-1877); Optical Isomers

Lec 26 - Van't Hoff's Tetrahedral Carbon and Chirality

Lec 27 - Communicating Molecular Structure in Diagrams and Words

Lec 28 - Stereochemical Nomenclature; Racemization and Resolution

Lec 29 - Preparing Single Enantiomers and the Mechanism of Optical Rotation

Lec 30 - Esomeprazole as an Example of Drug Testing and Usage

Lec 31 - Preparing Single Enantiomers and Conformational Energy

Lec 32 - Stereotopicity and Baeyer Strain Theory

Lec 33 - Conformational Energy and Molecular Mechanics

Lec 34 - Sharpless Oxidation Catalysts and the Conformation of Cycloalkanes

Lec 35 - Understanding Molecular Structure and Energy through Standard Bonds

Lec 36 - Bond Energies, the Boltzmann Factor and Entropy

Lec Last - Potential Energy Surfaces, Transition State Theory and Reaction Mechanism

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