Course Identification

Mathematics for Physics

This course is specifically designed to enhance knowledge and improve understanding of high school teachers in fundamental aspects of quantum mechanics.

1. Introductory Review of Classical and Basic Quantum Mechanics. Classical kinematics and dynamics. Historical motivation behind quantum mechanics. De Broglie waves and Schrodinger equation for them. Interpretation of the wave function. Measurements and observables. Quantum rules. Heisenberg uncertainty principle. Feynman formulation. Simple quantum mechanical systems - potential well, oscillator, rotor, reflection off and transmission through a barrier. Hydrogen atom. Density matrix. Spin, identical particles and Pauli principle.
2. Quantum Mechanics of Light. From a guitar to EM field - waves as a collection of harmonic oscillators. What was the problem with the black body radiation? Quanta of wave oscillators - phonons of vibration, photons of light, etc. What is the electric field of a photon? Schrodinger equation as a classical equation for the matter quanta -- modern Bose Einstein condensates.
3. How is light emitted and absorbed? Light matter interaction. Dipole limit. Selection rules. Higher multipoles and their selection rules (very briefly). Radiative transitions in simple atoms.
4. States of light . Which light do lasers emit? What does the sun emit? Ordinary lamps? Coherent, number, squeezed and thermal states of light
5. Quantum Mechanics of Atoms. Review of the hydrogen atom and its degeneracies. Atoms with more than one electron. Hartree-Fock Approximation. Examples of atomic spectra.
6. [6] Quantum Mechanics of Molecules. Separation of nuclear and electronic motion - Born Oppenheimer approximation. Electronic levels. Molecular vibrations. Molecular rotations.

Upon successful completion of this course students should be able to:

1. Demonstrate knowledge of basic concepts and of formal structure of Quantum Mechanics
2. Describe the quantization of the electromagnetic field and the quantum mechanics of the realistic atomic and molecular systems.
3. Explain why the EM field appears as a collection of photons and how they interact with matter.
4. Describe how the Quantum Mechanics explains the structure of many electron atoms and the details of the periodic table of elements.
5. [5] Discuss the spectra and behaviours of simple molecules.

[1] Lecture notes (provided by the lecturer)
[2] D. Griffiths, Introduction to Quantum Mechanics