Suggested Curriculum for Physics - Quantum Mechanics
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The QuantumChemistry package in Maple allows physics students to perform quantum calculations on atoms and molecules and represents a powerful tool for introducing, exploring, and applying concepts encountered throughout the physics curriculum. The aim of these lessons is to provide students and/or instructors ways to interact with selected topics using the QuantumChemistry package exclusively within Maple with no need to collate multiple software packages! Lessons are written to emphasize learning objectives rather than Maple coding. However, in order to show students and instructors how the calculations are set up, each lesson contains the Maple syntax and coding required to interact with the selected topic. In some cases, questions are asked of the student with the answer provided as a subsection. As such, each lesson can be used 'as-is' or modified as desired to be used by students in a classroom setting, laboratory setting, or as an out of class guided inquiry assignment.
While lessons are largely independent of each other and may be done in any order, the following suggestion corresponds to the ordering of topics typically encountered in atomic and molecular physics. Lessons 1 and 2 (Blackbody Radiation and Photoelectric Effect) correspond to early experiments related to the quantization of energy. Lessons 3 and 4 (Particle in a Box (H chain) and Particle in a Box (Dyes) ) involve the Schrödinger equation and its solutions with applications to a chain of hydrogen atoms and absorption spectra of conjugated dyes (a common undergraduate physical chemistry experiment), respectively. Lesson 5 (Vibrational Motion and the Harmonic Oscillator) explores vibrational motion and the harmonic oscillator approximation for several diatomic molecules. Lesson 6 (Variational Theorem) introduces the variational theorem and related basis set / matrix methods for the particle in a box and fir the Morse oscillator for hydrogen chloride. Lesson 7 (Molecular Orbitals) focuses on molecular orbital theory as applied to hydrogen fluoride. Lesson 8 (Koopman's Theorem and Drug Activities) introduces Koopman's theorem for approximating ionization energies with applications to small isoelectronic binary compounds and to non-steroidal anti-inflammatory drug (NSAID) activities. Lesson 9 (Geometry Optimization and Normal Modes) explores a very common quantum mechanical calculation, geometry optimization, and a subsequent normal mode analysis of the vibrational modes in the molecule. Lesson 10 (Vibrational Spectroscopy) uses basis set / matrix methods introduced in Lesson 6 to calculate a potential energy surface for a diatomic and then calculates the rovibrational energy levels and associated Q- and R-branches.
1. Blackbody Radiation
This lesson compares Rayleigh-Jeans and Planck distributions for blackbody radiation and applies Planck's distribution to calculate the temperature of the universe.
2. Photoelectric Effect
This lesson uses the photoelectric effect to find an 'empirical' fit to Planck's constant.
3. Particle in a Box (H-atoms)
This lesson explores solutions (energies and wavefunctions) to the Schrödinger equation for a particle in a symmetric box and applies the particle in a box model to a chain of hydrogen atoms.
4. Particle in a Box (Dyes)
Similar to Lesson 3, this lesson focuses on the solutions to the Schrödinger equation for a particle in a box with an application to absorption spectra of conjugated dye molecules.
5. Vibrational Motion and the Harmonic Oscillator
This lesson explores vibrational motion and the harmonic oscillator approximation for several diatomic molecules.
6. Variational Theorem
This lesson explores the variational theorem using particle in a box and the Morse oscillator for hydrogen chloride.
7. Molecular Orbitals
This lesson emphasizes the linear combination of atomic orbitals (LCAO) approach to calculating molecular orbitals for hydrogen fluoride.
8. Koopman's Theorem and Drug Activities
This lesson uses Koopman's theorem to approximate ionization energies of small binary compounds.
9. Geometry Optimization and Normal Modes
This lesson involves finding the optimum geometry for a triatomic and the associated vibrational normal modes.
10. Vibrational Spectroscopy
This lesson allows students to go beyond a normal mode analysis to calculate ab initio potential energy surface and associated rovibrational energies of a diatomic using a variational matrix method.
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