Quantum Mechanics I (for Quantum Masters

This course is the first course of a two-semester sequence that provides a rigorous, Master's-level foundation in quantum mechanics, uniquely structured for an interdisciplinary cohort of physicists, engineers, and computer scientists. Bypassing the traditional historical approach, the fall semester utilizes a "spins-first" pedagogy incorporating aspects of information theory but grounded in foundational physical experiments. By beginning with the Stern-Gerlach experiment and discrete matrix mechanics, students immediately engage with the physics of quantized angular momentum, magnetic moments, and quantum measurement—leveraging the strong linear algebra backgrounds of engineering and computer science students. Crucially, while sharing the mathematical language of quantum information, this sequence is firmly a physics course grounded in the natural world. From discrete spins, the curriculum smoothly transitions to modeling concrete physical problems, introducing continuous time evolution governed by physical Hamiltonians, wave mechanics in continuous space, and the quantum harmonic oscillator. Throughout this progression, abstract concepts are consistently paired with their modern hardware counterparts—such as utilizing trapped ions and NV centers to illustrate discrete spins, or superconducting LC circuits to motivate the harmonic oscillator. This approach pushes traditional physics students toward a deeper understanding of abstract operator algebra, while ensuring those aiming for PhD programs in physics or materials science build a robust, physical understanding of energy and dynamics.