"Learning goals: at the end of the course, the student
- understands the concept of propositional calculus related to observations arising from physical experiments;
- understands how the propositional calculus related to QM experiments leads to the Hilbert space formalism;
- is able to apply linear operator (Sturm-Liouville) theory to find, characterise or analyse eigenstates of the Hamiltonian for single particle in one-dimension;
- understands the origin of some of the conceptual problems related to systems of two particles;
- is able to understand and criticise recent papers dealing with the concepts entanglement, locality, realism and/or hidden variables"
"The aim of (mathematical) modelling is to establish correspondences between aspects in the real world and symbols in some abstract language. Reasoning using this language can lead to new statements in this language, corresponding to predictions about how the real world could behave, which can be verified using experiments.|
In order to be useful, the structure of the mathematical model should correspond to the structure of the observations about the real world. In a most basic form, such observations are propositions, like ""the position is between 1 and 2"", ""the polarisation is vertical"", or, more complicated, combinations like ""the position is between 1 and 2 and the polarisation is vertical"". In general, the propositions you can make about the world forms a calculus; the structure of this calculus has to be reflected in the mathematical model.
Starting from some fundamental experimental results we indicate why the mathematical structure of classical theories differs from that of quantum mechanics. We discuss the concepts of state and observables, and how they are represented in the mathematical model. You will learn why the Hilbert space formalism is a natural formalism for quantum mechanics. In the 5 EC version of this course, the Hilbert space formalism is elaborated to cover Sturm-Liouville equations.
Having established a mathematical model, the next questions are whether such model covers all relevant aspects of reality (is it complete?), and whether all artefacts within such a model necessarily correspond to aspects of reality (is too big?). We will illustrate this using the discussion on locality and realism, arising from the concept of entanglement that is a natural artefact in the mathematical theory."
External students who are interested with this elective please contact email@example.com