One-Dimensional Wave Functions

Lecture Description

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.

Course Description

This is the first semester in a two-semester introductory course focused on current theories of structure and mechanism in organic chemistry, their historical development, and their basis in experimental observation. The course is open to freshmen with excellent preparation in chemistry and physics, and it aims to develop both taste for original science and intellectual skills necessary for creative research.

Related Resources

Lecture Resources

Course Index

1. How Do You Know: Divine or Human Authority vs Logic and Experiment
2. Force Laws, Lewis Structures and Resonance
3. Double Minima, Earnshaw's Theorem, and Plum-Puddings
4. Coping with Smallness and Scanning Probe Microscopy
5. X-Ray Diffraction
6. Seeing Bonds by Electron Difference Density
7. Quantum Mechanical Kinetic Energy
8. One-Dimensional Wave Functions
9. Chladni Figures and One-Electron Atoms
10. Reality and the Orbital Approximation
11. Orbital Correction and Plum-Pudding Molecules
12. Overlap and Atom-Pair Bonds
13. Overlap and Energy-Match
14. Checking Hybridization Theory with XH3
15. Chemical Reactivity: SOMO, HOMO, and LUMO
16. Recognizing Functional Groups
17. Reaction Analogies and Carbonyl Reactivity
18. Amide, Carboxylic Acid and Alkyl Lithium
19. Oxygen and the Chemical Revolution (Beginning to 1789)
20. Rise of the Atomic Theory (1790-1805)
21. Berzelius to Liebig and Wöhler (1805-1832)
22. Radical and Type Theories (1832-1850)
23. Valence Theory and Constitutional Structure (1858)
24. Determining Chemical Structure by Isomer Counting (1869)
25. Models in 3D Space (1869-1877); Optical Isomers
26. Van't Hoff's Tetrahedral Carbon and Chirality
27. Communicating Molecular Structure in Diagrams and Words
28. Stereochemical Nomenclature; Racemization and Resolution
29. Preparing Single Enantiomers and the Mechanism of Optical Rotation
30. Esomeprazole as an Example of Drug Testing and Usage
31. Preparing Single Enantiomers and Conformational Energy
32. Stereotopicity and Baeyer Strain Theory
33. Conformational Energy and Molecular Mechanics
34. Sharpless Oxidation Catalysts and the Conformation of Cycloalkanes
35. Understanding Molecular Structure and Energy through Standard Bonds
36. Bond Energies, the Boltzmann Factor and Entropy
37. Potential Energy Surfaces, Transition State Theory and Reaction Mechanism