After completing this module a student should be able to:
Understand the fundamental concepts of quantum mechanics, such as the Schrödinger equation, wave function, quantization, and expectation values
Understand the quantum mechanical description of a particle’s translational, rotational and vibrational motions and discuss the corresponding wavefunctions and energy levels
Grasp the concepts of spin and angular momentum and their quantization, and explain the Zeeman affect and spin-orbit coupling
Understand how quantum mechanics can be used to describe the electronic structure of hydrogenic atoms and many-electron atoms
Understand the origin of atomic and molecular spectra and discuss the selection rules governing such spectra
Predict the thermodynamic properties of a gas in the ideal state from the knowledge of a few literature data for the vibrational frequencies and the geometry of the molecule
Apply principles of Statistical Thermodynamics in order to compute equilibrium constants for chemical reactions
At the end of the course the student will have further developed the following skills/competences:
- Ability to solve the Schrödinger equation to obtain wave functions for some simple, physically important one-dimensional systems, and to apply the technique of separation of variables to solve problems in more than one dimension.
- Ability to apply operators to the wavefunction to obtain information about a particle's physical properties such as position, momentum and energy.
- Ability to determine the electronic structure of an atom according to the modern quantum theory and to relate it to its properties and interactions with light.
- Ability to interpret atomic spectra.
- Ability to interpret rotational and vibrational spectra of simple molecules and obtain information related to their physical properties.
There are no prerequisite courses. The students are expected to master the basic mathematical skills that will be required throughout the course (use of complex numbers and functions, simple differential equations, integrals, and basic linear algebra).
- Introduction to the Quantum Theory. Classical mechanics. The dynamics of microscopic systems. Quantum mechanical principles.
- Techniques and Applications. Translational motion. Vibrational motion. Rotational motion.
- Atomic Structure and Atomic Spectra. The structure and spectra of hydrogenic atoms. The structures of many-electron atoms. The spectra of complex atoms. Term symbols and selection rules. The effects of magnetic fields.
- Molecular Structure and Molecular Spectra. Molecular orbital theory. The hydrogen molecule-ion. The structures of diatomic molecules. The structures of polyatomic molecules. Rotational spectra of diatomic and polyatomic molecules. Vibrational spectra of diatomic molecules. Introduction to electronic transitions and electronic spectra.
- Introduction to statistical thermodynamics. Basic concepts and overall goal. Thermodynamic equilibrium and equilibrium statistical ensembles with emphasis to NVE and NVT ones.
- Canonical partition function. Boltzmann distribution. Canonical ensemble and applications in the calculation of thermodynamic properties for ideal systems. Translational, rotational, vibrational, and electronic contributions to the molecular canonical partition function. Fluctuations. 3rd thermodynamic law and residual entropies.
- Calculation of equilibrium constants for chemical reactions. Application to dissociation reactions.
- Canonical partition function and non-ideal systems. Configuration integral. Models for inter-molecular potential energy and applications. Calculation of excess thermodynamic properties. Derivation of the virial constitutive equation.
Lectures (Power Point presentations). Lectures notes and other didactic material are made available to the students in electronic format. Weekly homework sets.
LECTURES: 4 h/w
RECITATION: 2 h/w
Total Module Workload (ECTS Standards):
3 written exams during the semester, final written and/or oral exam.
- P.W. Atkins and J. de Paula, “Physical Chemistry”, 9th Edition, Oxford University Press, 2010 (Greek translation, 2014).
- Στέφανος Τραχανάς, “Στοιχειώδης Κβαντική Φυσική”, Πανεπιστημιακές Εκδόσεις Κρήτης, 2012.
- V.G. Mavrantzas, “Statistical Thermodynamics”, Hellenic Open University, Patras (2001).