A concrete introduction to the abstract principles of quantum mechanics.
In this advanced elective, the student encounters Stern Gerlach-type experiments that require new ideas of quantization, probability, and measurement. This leads to wave-particle duality and as a natural consequence, uncertainty principles. Schrodinger equation is introduced and a way to calculate the eigenstates represented as wave functions is illustrated for simple one-dimensional potential systems including harmonic oscillator. All the ideas collected so far are applied on a real system – the hydrogen atom. Identical particles are treated and extended to spin-related statistics.
Mathematical development takes place alongside the conceptual development and some space is provided for the student to learn the essentials and apply them. Some advanced methods such as angular momentum addition, scattering, approximation methods (perturbation, variational principle) will be briefly surveyed.
All attempts shall be made to demystify the ‘counter-intuitive’ quantum world by collecting the core ideas and separating what can be considered or modelled classically in terms of wave or particle phenomena and what cannot be achieved in such a manner (e.g. entanglement).