Quantum Mechanics

This 12 lecture series covers the foundational principles of quantum mechanics, the bedrock for physics and its subdisciplines. Some understanding of calculus and differential equations is assumed.

1. Introduction: What is classical mechanics? What is quantum mechanics? Which people will never need QM?  Why is QM ever needed?  What led to the invention of QM? Why is QM so different and difficult?

2. Basics: Discrete states of a quantum system;  Superposition principle; Schrodinger's Cat;  The wavefunction of a particle; Taking averages.

3. Observables and Operators: Planck's Constant;  Wave-Particle Duality;  Observables and Operators;  Eigenvalues and Eigenfunctions; So-called "derivations" of the Schrodinger Equation.

4. The Free Particle in Quantum Mechanics: The Free Particle in CM;  The Free Particle in QM;  Eigenvalues and Eigenfunctions  for a Free Particle; Particle in an Infinite Well.

5. Expanding in Eigenfunctions: Eigenfunctions of the infinite well; Determining expansion coefficients;  Interpreting coefficients quantum mechanically;  How a wavefunction changes with time.

6. Quantum Simple Harmonic Oscillator: Why is the SHO so important?  The Schrodinger Equation for the SHO;  Solving the Oscillator Schrodinger Equation;  Averages of Kinetic/ Potential Energies;  Understanding the results.

7. Bound and Unbound States: Bound states; Unbound states; Wavefunction nodes and Kinetic Energy; Physical Examples.

8. Quantum Mechanical Tunneling: What is tunneling?probability current; steps and barriers; alpha decay of a nucleus; scanning electron microscope.

9. Angular Momentum - I: classical angular momentum; transition to quantum mechanics; quantization of angular momentum; quantization of energies; generating translations and rotations.

10. Angular Momentum - II: angular momentum in 3-D; commutation rules; quantization of angular momentum; spherical harmonics; application to rigid rotator.

11. Hydrogen Atom - I: the 1913 picture of the H-atom (Bohr atom); a very rough calculation of the size and energy; Schrodinger Equation (L=0 case only); solutions of the SE; understanding the solutions.

12. Hydrogen Atom - II: the H-atom in polar coordinates; review of angular momentum in 3-D; energies and eigenfunctions; understanding the solutions; multi-electron atoms.