Παρουσίαση/Προβολή

Prerequisites/Prior Knowledge

Students are expected to have successfully completed Φ303 (Κβαντομηχανική Ι). While the first lecture will review some material from the previous semester, prior familiarity with the mathematical (operator) formalism of quantum mechanics is essential. A working knowledge of linear algebra, as well as ordinary and partial differential equations, is assumed.

Course Syllabus

The course consists of roughly five parts

1. I will quickly review the operator formalism of the previous semester. In addition, I will show that the Schrödinger equation is not a fundamental axiom but instead follows from the symmetries of the theory. This topic is almost always omitted, even from many graduate courses, but I believe it is essential for a deeper understanding of Quantum Mechanics. It will also be necessary for understanding the final part of the course (if we get there). This will be the most advanced conceptual portion of the course. Afterwards, we will return to the textbook (see below) and cover Sections 9–14 (and possibly Section 15).

2. In the previous semester, students learned how to solve simple systems exactly, such as the harmonic oscillator and the non-relativistic hydrogen atom. In most realistic situations, however, an analytical solution of the Schrödinger equation is not possible, and one must instead rely on approximate methods. In this part of the course, we will develop the general formalism for such methods and examine several examples.

3. Applications: We will then apply the above methods to understand famous phenomena like the photoelectric effect.

4. Fundamentals and Quantum Computing: In this part of the course, we will discuss the probabilistic interpretation of quantum mechanics. If time permits, we will also provide a brief introduction to quantum computing.

5. Relativistic Quantum Mechanics: In the second part, we will study certain corrections to the hydrogen atom Hamiltonian without discussing their origin. If time permits and students are interested, we will also provide a brief introduction to relativistic quantum mechanics and explain the origin of these terms.

Textbooks

Assuming that everyone is comfortable with reading books in Greek, we will follow the book "Κβαντομηχανική ΙI'' by Σ. Τραχανάς. If that's not the case we will adjust. Material for the first and last part will be provided.

Some additional books are:

- "Quantum Mechanics: A Modern Development", L. E. Ballentine.

- "Introduction to Quantum Mechanics'', D. J. Griffiths & D. F. Schroeter.
- "Principles of Quantum Mechanics'', R. Shankar.
- "Εισαγωγή στην Κβαντομηχανική'', Κ. Ταμβάκης.
- "Modern Quantum Mechanics'', J. J. Sakurai & J. Napolitano.
- "Προβλήματα Κβαντομηχανικής'', Σ. Τραχανάς.
- "Κβαντική Μηχανική'', N. Zettili.

Homework

Homework problems will be assigned regularly but they will not be part of the grade. Students will be expected to solve them and we will have an extra class every week to discuss them (regarding the time we will coordinate in the first lecture).

Grades

The grade will be based on the final exam. If the number of students is not very large, we will also have an oral exam where we will discuss the mistakes students made in the written exam which can boost their grades.

Announcements

All course-related announcements will be made through the e-class portal.

To contact me direct, send me an email or talk to me after class.