Academic Year:
2021/22
32523 - MATHEMATICAL FUNDATIONS OF QUANTUM MECHANICS
This is a non-sworn machine translation intended to provide students with general information about the course. As the translation from Spanish to English has not been post-edited, it may be inaccurate and potentially contain errors. We do not accept any liability for errors of this kind.
The course guides for the subjects taught in English have been translated by their teaching teams
Teaching Plan Information
Code - Course title:
32523 - MATHEMATICAL FUNDATIONS OF QUANTUM MECHANICS
Degree:
616 - Máster en Química Teórica y Modelización Computacional (2013)
651 - Máster Erasmus Mundus en Química Teórica y Modelización Computacional
666 -
748 -
751 - Máster en Química Teórica y Modelización Computacional Europeo
762 -
Faculty:
104 - Facultad de Ciencias
Academic year:
2021/22
1.1. Content area
Mathematical Foundations of Quantum Mechanics
1.2. Course nature
616 - Compulsory
762 - Compulsory
666 - Training Supplement
651 - Compulsory
748 - Compulsory
751 - Compulsory
1.3. Course level
616 - Máster (EQF/MECU 7)
666 - Doctorado (EQF/MECU 8)
762 - Máster (EQF/MECU 7)
651 - Máster (EQF/MECU 7)
748 - Máster (EQF/MECU 7)
751 - Máster (EQF/MECU 7)
1.4. Year of study
751 - Máster en Química Teórica y Modelización Computacional Europeo: 1
651 - Máster Erasmus Mundus en Química Teórica y Modelización Computacional: 1
748 - : 1
762 - : 1
666 - : 99
616 - Máster en Química Teórica y Modelización Computacional (2013): 1
1.5. Semester
616-Annual o First semester
666-Annual o First semester
762-Annual o First semester
651-Annual o First semester
748-Annual o First semester
621-Annual
751-Annual o First semester
1.6. ECTS Credit allotment
5.0
1.7. Language of instruction
English
1.8. Prerequisites
There are no previous prerequisites.
1.9. Recommendations
There are no recommendations.
1.10. Minimum attendance requirement
Attendance is mandatory.
1.11. Subject coordinator
Antonio Picon Alvarez
1.12. Competences and learning outcomes
1.12.1. Competences
BASIC AND GENERAL
CB6 – Students possess and understand knowledge that provides a basis or opportunity to be original in the development and/or application of ideas, often in a research context.
CB7 - Students know how to apply the acquired knowledge and their problem solving capacity in new or little known environments within broader (or multidisciplinary) contexts related to their area of study.
CB8 - Students are able to integrate knowledge and face the complexity of making judgments from information that, incomplete or limited, includes reflections on social and ethical responsibilities linked to the application of their knowledge and judgments.
CB9 - Students know how to communicate their conclusions and the knowledge and reasons that support them to specialized and non-specialized audiences in a clear and unambiguous way.
CB10 - Students possess the learning skills that allow them to continue studying in a way that will be self-directed or autonomous.
CG01 - Students are able to foster, in academic and professional contexts, technological and scientific progress within a society based on knowledge and respect for: a) fundamental rights and equal opportunities between men and women, b) The principles of equal opportunities and universal accessibility for persons with disabilities, and c) the values of a culture of peace and democratic values.
CG02 - Students are able to solve problems and make decisions of any kind under the commitment to the defense and practice of equality policies.
CG03 - Students are able to work as a team both at multidisciplinary level and with their own peers respecting the principle of equality of men and women.
CROSS-COMPREHENSIVE
CT01 - Students are able to adapt their selves to different cultural environments by demonstrating that they are able to respond to change with flexibility.
CT02 - Students are organized at work demonstrating that they know how to manage their time and resources.
SPECIFIC
CE01- Students demonstrate their knowledge and understanding of the facts applying concepts, principles and theories related to the Theoretical Chemistry and Computational Modeling.
CE04 - Students understand the theoretical and practical bases of computational techniques with which they can analyze the electronic, morphological and structural structure of a compound and interpret the results adequately.
CE12 – Students are familiar with the fundamental postulates of Quantum Mechanics necessary for a good understanding of the most common methods used in quantum chemistry.
CE17 - Students understand and manage the mathematical tools required for the development of theoretical chemistry both in fundamental aspects and applications.
1.12.2. Learning outcomes
To understand the mathematical tools needed to develop the main methods in Quantum Mechanics and to understand the main concepts and applications.
1.12.3. Course objectives
-
1.13. Course contents
Part I
1 - Introduction. Solution of Schrödinger equation in simple systems
2 - Basic algebra
3 - Functional Spaces
4 - Approximate Methods in Quantum Chemistry: Variational Principle and Time-independent Perturbation Theory
5 - Independent and Identical Particles
6 - Angular momentum, spin.
7 - Main theorems in Quantum Mechanics
8 - Composition of Angular Momenta.
Part II
9- Pure states and mixed states
10- Postulates of Quantum Mechanics
11- Compatible and incompatible observables
12- Density operators
13- Time evolution pictures
14- Time dependent perturbation theory
15- Compound systems. Correlation and entanglement
16- Discrete representations. Basis changes
17- Position and momentum representations
18- Second quantization formalism
19- Reduced density operators and matrices. Natural spinorbitals
1.14. Course bibliography
a) Very basic level
Quantum Chemistry (6th edition 2008). Ira N Levine. Prentice Hall.
Student Solutions Manual for Quantum Chemistry. Ira N Levine.
Molecular Quantum Mechanics (5th Edition 2010). Peter W. Atkins , Ronald S. Friedman. Oxford University Press.
Quantum Chemistry (2nd edition 2008). Donald A. McQuarrie. University Science Books.
Problems and Solutions for Mcquarrie's Quantum Chemistry. Helen O. Leung, Mark Marshall.
b) Recommended level
Quantum Mechanics, Volume 1 and 2. Claude Cohen-Tannoudji, Bernard Diu, Frank Laloe. Wiley-Interscience (2005).
Quantum Mechanics (2nd Edition, 2000). B.H. Bransden, C.J. Joachain. Benjamin Cummings.
Problems and Solutions in Quantum Chemistry and Physics. Charles S. Johnson Jr., Lee G. Pedersen. Dover Publications (1987).
Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory. Attila Szabo, Neil S. Ostlund.Dover Publications (1996).
c) Advanced level
Quantum Mechanics Non-Relativistic Theory, Third Edition: Volume 3. L. D. Landau, L. M. Lifshitz.
Quantum Mechanics (2 Volumes in 1). Albert Messiah.
Quantum Mechanics (2 volumes). Alberto Galindo, Pedro Pascual. Springer (1991).
2. Teaching-and-learning methodologies and student workload
2.1. Contact hours
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# hours
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Contact hours (minimum 33%)
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43
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Independent study time
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82
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2.2. List of training activities
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Activity
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Nº hours
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Lectures
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31
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Seminars
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12
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Practical sessions
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Clinical sessions
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Computer lab
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Laboratory
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Work placement
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Supervised study
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Tutorials
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Assessment activities
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Other
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Lecture: The Professor will deliver lectures about the theoretical contents of the course during two-hour sessions. The presentations will be based on the different materials available at the Moodle platform.
Network teaching: All the tools available at the Moodle website (https://posgrado.uam.es) will be used (uploading of teaching materials, utilization of work team strategies, wiki, blogs, e-mail, etc.).
Online Seminars: After the lecturing period, online seminars between the Professor and the students will be arranged at the virtual classroom in order to discuss the results being obtained, the potential problems and difficulties in using the various methodologies as well as to supervise the preparation of the required reports.
Tutoring sessions: The professor can organize either individual or group tutoring sessions about particular topics and questions raised by students.
3. Evaluation procedures and weight of components in the final grade
3.1. Regular assessment
The knowledge acquired by the student will be evaluated along the course. The educational model to follow will emphasize a continuous effort and advance in training and learning.
The final student mark will be based on exercises that must be done during the course. The next criteria will be followed for assessment of student exercises:
- 60% from a set of proposed exercises.
- 40% from the student reports, discussions between the student and professor in tutoring session and seminars
3.1.1. List of evaluation activities
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Evaluatory activity
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%
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Final exam
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60
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Continuous assessment
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40
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3.2. Resit
The student will have to repeat those exercises not presented during the course and repeat those incorrectly done. The student will also do a final exam. The student mark will be obtained from:
100% from the student exercises presented and discussions between the student and the teachers.
3.2.1. List of evaluation activities
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Evaluatory activity
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%
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Final exam
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100
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Continuous assessment
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4. Proposed workplan
Please, check the official schedule posted on the master website.