Throughout our time at SigmaNext, we will study an axiomatic formulation of quantum mechanics. We will see how phenomena such as the uncertainty principle and energy quantization appear in quantum mechanical systems and try to answer the question: "What differentiates a classical system from a quantum one?" In the process, we will introduce new mathematical tools from linear algebra and study common quantum mechanical systems (harmonic oscillator, two-level systems, etc.). Armed with the ability to perform calculations, we will discuss the philosophical questions that are posed by Quantum Mechanics and understand what many physicists have been puzzled by since the beginning of the 20th century.
Pre-requisites:
- being comfortable with algebraic manipulations, some familiarity with classical mechanics, and conceptual familiarity with Bohr-Rutherford models and atomic orbitals.
- Some knowledge of probability (what are expectation value and standard deviation) is preferred but not required.