Quantum Mechanics Ii

AY2022/2023 Semester 1

Most introductory courses or books in QM start off with special systems (for example infinite square well) and derive its wave function in position representation from the Schrodinger?s equation. Although this approach may be intuitive due to its physical setup, it tends to give the wrong impression that wave functions are fundamental objects in QM. In actual fact, wave functions are just the different representations of the state (ket in Dirac notation) of the system. One can always choose other representations or even not choose a representation. This course aims to unteach wave mechanics and free you of particular representations and work with the formalism directly. You will explore the logical development of Quantum Mechanics (QM) formalism and develop QM systematically from finite to infinite dimensions in three parts. Part 1 aims to give a complete and systematic run-down of basic quantum kinematics and quantum dynamics so that you have a working understanding of quantum mechanics for finite-dimensional and infinite dimensional systems. The concept of measurement will also be covered. This provides probabilistic results for experiments. Part 2 aims to discuss symmetry within QM. Rotational symmetry (angular momentum is the generator of rotations) is the main and very important example. The rotational symmetry in Hydrogenic atoms will also be discussed, which will also introduce you to 3D QM. Part 3 adds on to the formalism for systems that cannot be solved exactly. These are real-life QM examples and the standard method to solve these systems is via perturbation for time-independent/dependent and non-degenerate/degenerate systems.