Quantum Mechanics from Linear Algebra
The mysterious and surprising predictions of quantum mechanics, such as uncertainty in measurement and the failure of determinism, can be best understood through the language of linear algebra. In this course we will use eigenvectors and eigenvalues, dot products, and the Cauchy-Schwarz inequality to develop the fundamental postulates of quantum mechanics and their predictions for the behavior of quantum systems. We will focus particularly on spin systems, which have applications to areas ranging from quantum computing to magnetic resonance imaging to quaternion methods for 3-D graphics and motion tracking. No prior physics experience is assumed apart from basic familiarity with concepts such as momentum, energy, and electric charge. (MATH 0122, MATH 0200, and introductory physics at the high school or college level.)