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First Semester 
Teaching style
Lingua Insegnamento

Informazioni aggiuntive

Course Curriculum CFU Length(h)
[60/58]  CHEMISTRY [58/10 - Ord. 2017]  CHIMICA 6 48


Knowledge and understanding: at the end of the course, the student will achieve knowledge and competence on the fundamental theories and numerical applications of quantum mechanics. The student will learn how to derive, interpret and apply the laws determining the structure and the spectroscopic characteristics and properties of atoms and molecules.
Knowledge application ability: at the end of the course, the student will be able to use the knowledge and interpretation capabilities within a logic and comprehensive framework in order to solve numerical problems and answer scientific questions in the field of quantum mechanics.
Judgment capacity: the course aims at training the student in problem solving and understanding notions, equations and results. The final goal is to make the student independent in taking decisions pertaining to the choice of the most appropriate approach for the given problem.
Communication skills: the student will be able to integrate concepts in a coherent framework and to express them appropriately, concisely and effectively in a talk and through the use of diagrams, graphs and formulas.
Learning skills: the student will acquire the ability to undertake further studies on quantum mechanics and spectroscopic techniques with sufficient autonomy.


It is important that the student is proficient in Chemistry. In addition, a good background of Physics and Mathematics is absolutely necessary, especially on: complex numbers and trigonometry, resolution of systems of linear equations, matrix algebra, function limits and series expansion, derivatives, integrals and solution of differential equations. Basics of numerical calculation complete the profile.


Introduction and Principles: Energy quantization; wave-particle duality; dynamics of microscopic systems; Schrödinger equation; the wave-function; Born interpretation of the wave-function; the information in the wave-function; Heisenberg uncertainty principle; postulates of quantum mechanics.
Techniques and Applications: translational motion of a free particle and of the particle in a box; translational motion in two or more dimensions; tunnel effect; vibrational motion (harmonic oscillator); rotational motion in two dimensions (particle on a ring); rotational motion in three dimensions (particle on a sphere); the spin.
Atomic Structure and Atomic Spectra: Structure and spectra of hydrogenic atoms; atomic orbitals and their energy; spectroscopic transitions and selection rules; structure of many-electrons atoms; the orbital approximation; self-consistent field orbitals; spectra of complex atoms: singlet and triplet states.
Molecular Structure: Born-Oppenheimer approximation; valence-bond theory (homonuclear diatomic molecules); molecular orbital theory; hydrogen molecule-ion; homonuclear and heteronuclear diatomic molecules; molecular orbitals of polyatomic systems; Hückel approximation.

Teaching Methods

The course provides 6 CFU of lectures with a total of 48 hours. Computer and a video-projector will be used, together with scientific plotting softwares, videos and the traditional blackboard. The topics will be presented by following the order of increasing complexity. Practical tutorials are also planned, aiming at developing students’ capability of understanding and solving specific numerical problems related to the presented topics. The exercises will be also exampling the typical problems given during the examination.
Due to the present epidemiologic situation, there will be the possibility for the lectures to be attended both in class and in web streaming, with automatic recording which will be made available to the students. Exercises will be possibly carried out through the available software and electronic devices.

Verification of learning

The examination comprises one written examination and a final colloquium. The written examination consists of 4 numerical problems of the same kind of those demonstrated during the lectures.
The examination will be a colloquium during which several exercises will be also submitted.

The written exam aims at verifying the acquired competence, in terms of:
- making logic connections among the different topics
- problem-solving capabilities related to basic problems of quantum mechanics.
The final colloquium aims at verifying:
- knowledge from a theoretical viewpoint
- capacity of presenting the topics in a concise and comprehensive way
- capacity of using a correct scientific language, together with formulas and graphs.

During the written exam (2 hours) only a non-plotting scientific calculator and the tables (Constants, Useful Formula, Orbitals) provided by the teacher will be allowed.
During the final colloquium (about 1 hour) questions will cover any of the topic presented during the course. The student will have to demonstrate to be able to present the topic by making use of a proper and scientifically correct and accurate language, together with the proper use of mathematical formula and plots.
In particular, both in the written and oral exams, the students will be asked to take care of the correctness of all the symbols and measurement unit involved.

Marks and final evaluation:
The conclusive mark will be assigned as a fraction of 30 (x/30) and it will be given by the average of the mark gained from the written exam and the colloquium.
The mark (x/30) of the written exam will be given by the average of the grade obtained in each of the 4 given exercises. The grade for each of the latter will be given accrding to the following scheme:

The exercise is correct and detailed in all the steps. The applied method is the more appropriate.
The exercise is quite correct but the method selected is not the more appropriate.
The results are affected by minor mistakes which are easy to identify (sign error or wrong constant value).
The results are affected by remarkable errors, but the exercise is set up correctly.
Bad errors. The exercise was not understood.

The mark to the final colloquium will take different factors into account:
a) Ability of oral and graphical communication
b) Scientific language
c) Contents knowledge
d) Ability in correlating notions

Consequently, the final mark can be (x/30):
- Sufficient (18-20) Modest communication abilities. Little acquisition of knowledge, superficial level, many gaps.
- Moderate (21-23) Acceptable communication abilities. Moderate acquisition of knowledge but lack of expatiation, few gaps.
- Good (24 to 26) Satisfactory communication abilities. Rather large wealth of knowledge, moderate in-depth, small gaps. Critical spirit and logical linking capability are clear.
- Outstanding (27-29) Remarkable communication skills. Extensive wealth of notions, high in-depth, marginal gaps. Synthesis ability and competence are clear.
- Excellent (30) Excellent communication skills. Very extensive and in-depth knowledge, irrelevant gaps. Competence and deductive skills are clear.

The praise is attributed to the candidates clearly above average, and whose notional, expressive, conceptual, logical limits, if any, as a whole are completely irrelevant.


P. Atkins, J. de Paula: Physical Chemistry, 8th edition, Oxford University Press

More Information

The slides projected during the lectures will be provided. Format will be low resolution pdf. They are merely intended as a study guideline. Slides are neither to be considered as alternative nor additional to the suggested text books in any way. A compendium of numerical exercises will be also provided in pdf format, together with their solution, solving method and comments. Finally, tables with useful physical quantities and mathematical expressions will be also provided as pdf.

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