Konstantinos Moulopoulos

To provide a broad and fairly coherent understanding of Modern Physics through methods of certain mathematical sophistication (undergrad level), and to develop students’ ability to actually apply these methods in order to obtain quantitative results (in closed analytical form) in particular physical situations.

The students will learn what the most fundamental secrets of Nature are, both at the “classical” and “quantum” level (together with currently existing uncertainties on certain issues/questions that still remain open), and will be trained on how to practically use mathematical methods and apply them to particular physical situations in order to obtain (analytical) results.

Elements of Lagrangian and Hamiltonian Mechanics (and reference to Hamilton-Jacobi formulation as preparation for the passage to Quantum Mechanics). Elements of Electromagnetism/Classical Electrodynamics (Maxwell-Lorentz theory) – Introduction to the Special Theory of Relativity.

Elements of Quantum Mechanics: quantum states as vectors - and observables as (self- adjoint) operators - in Hilbert spaces, position and momentum representations and Fourier transforms, physical meaning of eigenvalues and eigenstates of Hermitian operators, solution of Schrödinger equation (viewed as an ordinary or partial differential equation) in simple quantum systems – Uncertainty Principle – Ehrenfest and Hellmann-Feynman theorems – Symmetries and Generators, gauge symmetry (and some of its nontrivial consequences)

20% Project, 40% Midterm Exam, 40% Final Exam.