Universidad de Jaén

Lesson 1.- Fundamentals of Quantum Mechanics (3 hours)

*Origins of Quantum Mechanics

*Operators. Eigenvalues equations.

*Hermitian operators. Commutation.

*The postulates of Quantum Mechanics.

*Superposition principle

Lesson 2.- Using Quantum Mechanics. Symple Systems (2 hours)

• The free particle in one dimension.
• The particle in a one-dimensional box.
• The particle in a two- and three-dimensional box. Degeneracy.
• Tunneling.
• Harmonic oscillator.

  Lesson 3. Approximation methods in Quantum Mechanics (3 hours)

• Variation method
• Linear variation method
• Perturbation method
• Perturbation theory for degenerate states
• Time-dependent perturbation theory

Lesson 4.- Angular momentum in Quantum Mechanics (3 hours)

• Angular momentum operators
• Rigid rotor
• Angular momentum coupling.
• Ladder operators. Coupled angular momentum eigenfunctions.

 Lesson 5.- Atomic structure (3 hours)

• The hydrogen atom
• Radial function properties
• Orbital angular momentum
• Electronic spin
• States of the hydrogen atom. Hydrogenlike orbitals.
• Electron configuration. Aufbau principle.
• Spin - Orbit interaction.

Lesson 6.- Electronic structure of diatomic molecules (3 hours)

• The hydrogen molecule and other homonuclear diatomic molecules. LCAO and VB methods
• Configuration interaction
• Molecular electronic terms
• Heteronuclear diatomic molecules

Lesson 7.- Electronic structure of polyatomic molecules (3 hours)

• Localized bonds
• Hybrid orbitals. Hybridization models.
• Delocalized bonds.
• Conjugated organic compounds. Hückel's method.

Lesson 8.- Interaction of electromagnetic radiation and matter (3 hours)

• Absorption and emission. Einstein's coefficients.
• Selection rules.
• Spectral line width and intensity. Lambert Beer's law
• Inelastic scattering. Raman effect

Lesson 9.- Vibrational and rotational spectroscopy of diatomic molecules (3 hours)

• Fundamentals of vibrations and rotations
• Centrifugal distortion
• Vibration-rotation coupling
• Vibrational anharmonicity. Selection rules
• Spectroscopic constants from vibrational spectra
• Analysis of microwave spectra

 Lesson 10.- Vibrational and rotational spectroscopy of polyatomic molecules (3 hours)

• Rotational spectroscopy of linear molecules
• Vibrational spectroscopy of polyatomic molecules
• Characteristic frequencies.
• Rotational states of non-linear polyatomic molecules

Lesson 11.- Electronic spectroscopy (3 hours)

• Atomic spectra. General features and selection rules
• Electronic spectra of diatomic molecules. Vibrational structure and Franck-Condon's principle
• Polyatomic molecules: chromophores and d-d transitions
• Emission spectra: Fluorescence and phosphorescence

Lesson 12.- Nuclear Magnetic Resonance (NMR) spectroscopy (3 hours)

• Nuclear spin
• Nuclear spin states. Energy
• Spin - spin coupling
• Electron Spin Resonance (ESR) spectroscopy
• External field effect: Stark and Zeeman effects

The theoretical lessons will be explained by using the master class method along 35-38 hours. In addtion, lists of numerical exercises will be delivered to the students and solved in class. Likewise, theoretical tests will be distributed through the virtual teaching platform to consolidate the most important concepts of the subject. Other activities could be proposed to the students.

Students with special educational needs should contact the Student Attention Service (Servicio de Atención y Ayudas al Estudiante) in order to receive the appropriate academic support

The subject will be assessed by using an exam that includes both questions of theory and numerical exercises. It amounts to 70% of the final marks for this subject.

In addition, the qualifications of both the class-proposed numerical exercises and theory tests will account for the remaining 30% of the final marks of the subject. Although these qualifactions will be only considered provided the exam is not failed.

Assessment of competences:

Exam - theory: Q5, Q1, C4

Exam - numerical exercises: Q1, Q2, Q5 C6

Class-proposed activities: C6, Q2, Q1, Q5