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ADVANCED QUANTUM PHYSICS
Module ADVANCED TOPICS IN QUANTUM PHYSICS

Academic Year 2026/2027 - Teacher: VINCENZO GRECO

Expected Learning Outcomes

The teaching proposes to provide a knowledge of quantum mechanics including its relativistic extension. In particular, the objective is to provide a knowledge of the main methods for understanding the quantum behavior of the physical systems of interest for modern physics, explicitly deriving the time-dependent pertubatical theory and the general elements of the quantum approach to the scattering process. Moreover, the teaching will allow to access to the more advanced formulations of quantum mechanics such as quantization of the electromagnetic field, the formulation of quantum mechanics in terms of Feynmann integrals and  the relativistic formulation of quantum mechanics with the Dirac and Klein-Gordon equations.

Upon completion of the course the student must be able to know the topics of the course and know how to derive through the necessary analytical steps the main results discussed in the course. It must also be able to apply this knowledge for the resolution of exercises on the behavior of quantum systems. The aim of the course is also that the student develops the critical capacity for the evaluation of the results obtained. This capacity will be developed during the course, focusing repeatedly on the physical meaning of the formulas obtained and on the methods for evaluating the order of magnitude of the expected results even before carrying out the full calculations.

Course Structure

The course lectures (3 CFU - 21 hours) are primarily based on the detailed derivation of formulas related to the topics covered and on discussing the meaning of the results obtained. Should teaching be delivered in blended or distance learning modes, necessary variations to what is stated above may be introduced in order to comply with the program outlined in the syllabus.

Required Prerequisites

A knowledge of the basic formulation of quantum mechanics and the one of the Quantum Physics course. It is important to have basic knowledge of mathematical analysis for the solution of integrals and differential equations and it is useful to know the residual method for the solution of complex function integrals.

Detailed Course Content

Particle as quantum states: neutral kaons and neutrino quantum oscillations.

Time dependent perturbation theory: instantaneous transitions in a two level system; Decays; Non-exponential decay law in quantum system: Zeno and Khalfin decays; energy level shifts and natural line width. Landau-Zerner transitions.

Textbook Information

1) J. J. Sakurai and J. Napolitano, Modern Quantum Mechanics, Ed. Addison-Wesley. / Meccanica Quantistica Moderna, Ed. Zanichelli (III edizione)

2) F. Schwabl, Advanced Quantum Mechanics, Ed. Springer.

3) Giuseppe Nardulli - Meccanica quantistica: applicazioni, vol II, Ed. Franco Angeli.

4) B. R. Holstein, Topics in Advanced Quantum Mechanics, Ed. Addison- Wesley.

Course Planning

 SubjectsText References
1Kaon neutral quantum oscillations3
2path integrals1) 4)
3line shape4)
4Casimir effect4)
5Lorentz Invariance of Dirac equation2)
6Solution of Dirac equation undr a potential2)

Learning Assessment

Examples of frequently asked questions and / or exercises

- Discuss the treatment of the decay of a quantum state inclusding the energy level shifts and natural line width.

- Discuss the solution of the harmonic oscillator in the Path-Integral formulation

- Derive the formula for the  energy assoicated to the Casimir effect.

- Make and ecample of quantum states with dofferent degree of  entanglement

- Demonstrate the Lorentz invariance of Dirac equation.

- Find the solution solution of Dirac equation in a square well.