%0 Generic
%A Rubio Peña, Javier
%T Lectures Notes on Quantum Physics II
%D 2023
%U https://hdl.handle.net/20.500.14352/103391
%X These lecture notes are intended for a one-semester course in Quantum Physics II at the Universidad Complutense de Madrid and assume prior exposure to the foundational elements of quantum theory, particularly the hydrogen atom and the harmonic oscillator as typically covered in a Quantum Physics I course. The course adopts a "spin first" pedagogical strategy, emphasizing the intrinsically quantum nature of spin-1/2 systems and avoiding usual classical analogies. This approach facilitates a direct and conceptually coherent introduction to the abstract formalism of quantum mechanics, encompassing state vectors in Hilbert spaces, linear operators, measurement theory, and time evolution. The spin-1/2 system serves throughout as a didactic and unifying framework for modeling a wide variety of quantum phenomena.The notes are structured to provide not only theoretical exposition but also extensive opportunities for active engagement with the material. To this end, each chapter is supplemented with a significant number of detailed examples that illustrate key results and computational methods. Furthermore, more than 150 exercises—both solved and proposed—are distributed throughout the text. The worked-out problems, included at the end of each chapter, are intended to consolidate core concepts and demonstrate standard techniques. The proposed exercises are carefully categorized to distinguish between those essential for examination preparation and those designed to encourage deeper conceptual understanding or formal exploration.Subsequent chapters expand the discussion to encompass composite quantum systems, mixed states, identical particles, and the algebraic structure of angular momentum, culminating in the treatment of approximation methods applicable to realistic physical systems. These include variational techniques, both time-independent and time-dependent perturbation theory, the WKB method, and relativistic corrections to bound-state problems. A broad spectrum of applications—ranging from molecular dynamics and atomic structure to neutrino oscillations, quantum Zeno dynamics, and atomic interactions in external fields—demonstrates the generality and utility of the formalism developed.
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