Quantum Physics III

The main goal of this course is to provide an understanding of the quantum laws that govern the processes giving rise to atomic and molecular structures. Since these differ very substantially from the principles of classical physics that the student has studied so far, it is necessary to review in depth fundamental concepts in both Mechanics and Electromagnetism.

LEARNING OUTCOMES:

The student shall demonstrate:

- That he/she understands the quantum laws governing the processes that give place to the atomic and molecular structures.

- That he/she knows the differences that arise in the study of quantum systems versus classical approaches.

- That he/she knows how to apply the relationships of quantum mechanics to solve the problems associated with calculations in atomic and molecular systems.

- That he/she understands and assimilates the orders of magnitude of the energies, lengths and characteristic units of the processes and forces that act between nucleons, nuclei and atoms.

ATOMIC STRUCTURE: Relativistic corrections to the atomic energies. Lamb displacement. Alkaline atoms. Helium atom. Multi-electronic atoms. Properties of the elements. The optical spectra and the X ray spectra in atoms. Hyperfine structure. Spin magnetic resonance. Nuclear magnetic resonances.

MOLECULAR BONDING AND CRISTAL STRUCTURE: Diatomic molecules. Particle in a double potential well. The molecule H2+. The hydrogen molecule: covalent binding. The model of molecular orbitals. Quantification of vibrational and rotational energies. Molecular spectra. Cristal structure binding. Schrödinger equation for periodic potentials. Band theory. Solid properties. Insulators, semiconductors and conductors.

SCATTERING: Basic concepts. Scattering by a potential well: partial waves and Born approximation. Resonances. Elastic scattering. Discrete level excitation. Ionization and charge exchange.

TEXTBOOKS:

- Weissbluth, M. Atoms and Molecules. Academic Press, Inc. (1978).

- Griffiths, D.J. and Schroeter, D.F. Introduction to Quantum Mechanics. Cambridge University Press (2018).

- Bransden, B.H. and Joachain, C.J. Physics of atoms and molecules. Longman Scientific & Technical (1990).

- Foot, C.J. Atomic Physics. Oxford University Press (2005).

- Sakurai, J.J. and Napolitano, J. Modern Quantum Mechanics (second edition). Cambridge University Press (2017).

- Eisberg e Resnik, Quantum Physics. Wiley.

- Sánchez del Río, C. Física Cuántica. Pirámide.

- Alonso e Finn, Fundamentos Cuánticos y Estadísticos. Fondo Educativo Interamericano.

- Alasdair I.M. Rae, Quantum Mechanics. Adam Hilger.

ADDITIONAL BOOKS:

- Weinberg, S. Lectures on Quantum Mechanics (second edition). Cambridge University Press (2015).

- Haken, H. e Wolf, H.C. Physics of Atoms and Quanta, Ed. Springer Verlag (1987).

- Bernstein, J. Modern Physics, Ed. Prentice Hall, 2000.

- Feynmann, R. Física Vol III, Mecánica Cuántica. Fondo Educativo Interamericano (1965).

BASIC:

CB1 – Starting from a High School education level, the student will steadily progress towards a broad coverage and understanding of physics. The level of understanding, usually supported by advanced textbooks, will include some introductory topics from current forefront scientific research in at least a specific field.

CB2 - The students will be able to apply this knowledge to their work or vocation in a professional way and master the competencies that are usually demonstrated through the elaboration and defense of arguments and the resolution of problems within their area of study.

CB3 - The students will be able to collect and interpret relevant data (usually within a specific area of study) to make judgments that include deep thinking on relevant social, scientific or ethical issues.

GENERAL:

CG1 - Understand the most important concepts, methods and results of the different branches of physics, with a historical perspective of their development.

CG2 – Be able to gather and interpret relevant data, information and results, to reach conclusions and to issue well-reasoned reports in scientific, technological or other areas that require knowledge of physics.

CG3 - Apply both the theoretical and practical knowledge acquired, together with excellent analysis and abstraction abilities, to a clear statement of relevant problems and to design good strategies for finding the solutions, both in academic and professional contexts.

SPECIFIC

CE1 - Have a good understanding of the most important physical theories paying special attention to their logical and mathematical structure, without forgetting their experimental support and the physical phenomenon that can be described through them.

CE2 - Be able to clearly handle very different orders of magnitude and make appropriate estimates to develop a clear perception of situations that, although physically different, show some analogy, allowing the use of known solutions to new problems.

CE5 - Understand the essentials of a process or situation and establish a working model for further study. Be able to carry out the required approximations in order to reduce the problem to a manageable level. Possess critical thinking to build physical models.

CE6 - Understand and master the mathematical and numerical methods most commonly used in physics.

CE8 - Be able to manage, search and use bibliography, as well as any source of relevant information, and apply it to research and technical development projects.

CROSS:

CT1 - Acquire excellent analysis and synthesis abilities.
CT2 - Have organizational capacity and planning.
CT5 - Develop critical reasoning.

An online Moodle course will be available on the USC Campus Virtual web page for the Quantum Physics III course. All relevant teaching material will be uploaded there. We will follow the teaching methodology described in the official Physics Grade Memorandum. All teaching, whether masterclasses or interactive seminars, will physically take place in the corresponding classroom. In the masterclasses all teaching material with the relevant calculations will be presented in detail, using projections and the blackboard. The students will be encouraged to ask questions. In the seminar-type classes, the problems will be solved and discussed preferentially by the students, who should have received the appropriate assignments well in advance.

The assessment, or grading, will consist of two complementary parts:

a) An evaluation made on a continuous basis during the course, with a maximum of 25% weight in the final grading. Individual or group tasks will be regularly assigned to the students using the Campus Virtual tools. Attendance to lectures and active participation during the interactive sessions will also be assessed.

b) A final written examination to be carried out in the classroom at the officially stipulated date.

The final written examination will have a minimum of 75% weight in the final grade, which shall be determined as follows. Let E be the numerical value (from 0 to 10) of the final written examination and let C be the numerical value (from 0 to 10) of the evaluation performed on a continuous basis. The final grade will then be computed as MAX( E, 0.75*E + 0.25*C ), where the MAX function delivers the maximum of the two values taken as arguments.

In the event of fraudulent behavior when performing the assigned qualification tasks, the USC official Regulation on the evaluation of the student’s performance shall be applied. Article 16 of that Regulation establishes that:

The fraudulent performance of any exercise or test required in the evaluation will imply the qualification of failure (suspenso) in the corresponding call, regardless of the disciplinary process that might be followed against the offending student. It will be considered fraudulent, among other things, to plagiarize works or to copy them directly from public sources without further reinterpretation and the appropriate citations of authors and sources.

The working time in presence of the teacher is 45 hours, classified as follows: 24 hours of master lectures in a large group; 18 hours of interactive sessions in small groups; 3 hours of tutoring for every student. The autonomous-individual worktime each student should devote to the course is estimated to be about 67.5 hours.

It is highly recommended to fully work out the assigned problems, especially as a method of self-evaluation system. As a general rule, the student will be required to provide numerical answers expressed in the appropriate system of units. Some of the basic formulas should be memorized to improve the understanding of the theoretical part and to solve the problems in a reasonable time.

Since all teaching notes will be available from the beginning of the course, it would be very beneficial for the student to do a first reading of the material before the formal presentation by the professor in the corresponding lecture.