Introduction to Special Relativity and Quantum Mechanics

Upon successful completion of this course, students will be able to:

Special Relativity

• explain what is meant by the principle of relativity, and give examples that appear to contradict this principle
• describe how Einstein's postulates of Special Relativity lead to the relativity of simultaneity
• transform spacetime coordinates and velocities between inertial reference frames using Lorentz transformations and velocity transformation
• describe and calculate the relativistic effects of time dilation, length contraction, and the relativistic Doppler effect
• use spacetime diagrams to graphically represent processes involving relativistic velocities
• resolve common paradoxes such as "the twins paradox" and the "pole in the barn" paradox 
• analyze dynamical processes using relativistic dynamics including particle decay and collisions
• explain the relations between mass, energy and momentum in relativity and describe the consequences of these relations to massless particles

 Quantum Mechanics

• explain the experimental evidence for the quantization of charge and light energy
• give qualitative predictions and explanations of the behaviour of simple quantum systems, such as the distribution of electrons in atoms and the spectrum of light emitted and absorbed by atoms
• explain the probabilistic interpretation of the wave function, and use the wave function to determine the expectated value of a measurement and the probability of various outcomes in simple quantum systems  
• explain how a wave packet can be generated using a quantum superposition of eigenstates and apply the Heisenberg Uncertainty Principle to determine the time evolution of a wave packet
• state the Schrödinger equation and the time-independent Schrödinger equation and explain how these equations govern the time evolution of wave functions
• verify solutions of the Schrödinger equation for a free particle and 1D potentials such as the infinite square well, the finite square well, the step potential and finite barrier (tunnelling) 
• qualitatively describe solutions to the 3D Schrödinger equation for the hydrogen atom (Coulomb potential), and the quantization of angular momentum

General

• demonstrate an understanding of popular science articles on current research in physics by the ability to answer questions about modern physics from curious friends and relatives
• value gaining a deeper understanding and appreciation of quantum mechanics and special relativity