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Teaching GuideTerm Faculty of Science |
| Grao en Nanociencia e Nanotecnoloxía |
 Subjects |
| Fundamentals of Quantum Theory |
| Contents |
| Identifying Data | 2023/24 | |||||||||||||
| Subject | Fundamentals of Quantum Theory | Code | 610G04015 | |||||||||||
| Study programme |
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| Descriptors | Cycle | Period | Year | Type | Credits | |||||||||
| Graduate | 1st four-month period |
Second | Obligatory | 6 | ||||||||||
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| Topic | Sub-topic |
| Introduction to Quantum Mechanics: Postulates | - Historical background. - Postulates of Quantum Mechanics. - Time-independent Schröndinger equation. - Importance of postulates: principles of correspondence, Heisenberg uncertainty and superposition of states |
| Translational motion: model of the particle in a box. | - Free particle. - The particle in a one-dimensional box: Wave functions and energy levels. - The particle in a two- and three-dimensional box: Separation of variables and degeneration. - Tunnel effect. - Applications of the particle in a box. Quantum wells, quantum wires and quantum dots |
| Vibrational motion: harmonic oscillator model | - Classic treatment of the harmonic oscillator. - Quantum oscillator treatment: Wave functions: Hermite polynomials. - Vibration energy: energy levels. - The harmonic oscillator as a model of vibration of molecules. - Anharmonicity |
| Rotational motion: rigid rotor model. | - Angular momentum in classical mechanics. - Angular momentum in quantum mechanics: Wave functions: Legendre polynomials. Spherical harmonics. - The rigid two-particle rotor: Rotational energy: energy levels. - Quantization of angular momentum. |
| Hydrogenoid atoms | - Resolution of the Schrodinger equation for the hydrogen atom or ion. - Radial and angular wave functions. - Energy levels. - Atomic orbital. - Radial distribution function. - Real wave functions: radial and angular representation. - Zeeman effect. |
| Approximation methods | - Schrondinger equation solving in systems of chemical interest. - Perturbation method. - Method of variations: variational theorem. - Linear variational functions: secular equations. - Applications of approximate methods to quantum chemistry |
| Multielectron atoms | - Study of the helium atom. - Slater orbitals. - Hartrree–Fock self-consistent field method. - Spin angular momentum. - Antisymmetry: Pauli's exclusion principle. - Periodic Table. - Electronic configuration. - Total orbital angular momentum: spin-orbit and jj couplings. - Hund's Rules. . Atomic spectroscopy. Atomic terms. Selection rules. - Atomic paramagnetism |
| Chemical bond. Introduction to the study of molecules. | - The molecular Hamiltonian. - Born-Oppenheimer approximation. - Molecular orbital theory and valence bond theory. - Application of the molecular orbital method to the hydrogen molecule ion. - Molecular orbitals: bonding and antibonding. - Homonuclear diatomic molecules. - Heteronuclear diatomic molecules. . Polar bond: electronegativity |
| Semiempirical methods. | - Ab initio and semiempiric methods. - Hartree-Fock method. Base sets. Electronic correlation. Method of interaction of configurations. Methods of density functional. - Pi-electronic approach. - Free electron method (FEMO). - Theory of molecular orbitals applied to conjugated and aromatic molecules: Hückel approximation. |
| Fundamentals of Statistical Mechanics. | - Fundamentals of the mechano-statistical method. - Bases of statistical thermodynamics. - Statistical thermodynamic study of ideal gases. - Statistical interpretation of the thermodynamic properties of solids. |
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