K7: To know the basic and central concepts and the most common methodologies of disciplines in which mathematical language and method are applied, such as physics, biology, economics, data science or cryptography. K8: To know the methods, tools and techniques of mathematics used to model, simulate and solve problems, identifying the different phases of the mathematical modeling process: formulation, analysis, resolution and interpretation of results. S2: Apply combined knowledge of mathematics and physics to model phenomena in areas such as biology, economics, or data science. "C2: Propose solutions to practical problems, using the most appropriate results and techniques, and critically analyze the results obtained, explaining the hypotheses and limitations of the models used. " C5: Abstract complex problems from real life or other sciences and formulate them in terms of mathematical equations, using variables, constants and parameters to make them understandable and solvable.

Origins of Quantum Mechanics. Blackbody radiation spectrum and Planck's Postulate. Einstein's theory of the photoelectric effect. The Compton effect. Broglie's principle and wave-particle duality. Atomic models of Rutherford and Bohr. Schrödinger's equation. Wave function. Born's interpretation: probability density. Expected values and measurement process. Energy, position and momentum. Principle of indeterminacy. Time-independent Schrödinger equation. Quantization of energy. Linked and unlinked states. One-dimensional problems. Solution for a free particle. Steps, wells and barriers of potential. The harmonic oscillator. Tunnel effect. Three-dimensional problems. Central potentials. Schrödinger's equation in spherical coordinates. Hydrogen Atom Solution.

A1: CLASSROOM LECTURES. Each subject has two weekly sessions: a lecture session, with more theoretical content, and a reduced session, with more practical content. In this session, the main theoretical content takes place. 100% de presencialidad / A2: FACE-TO-FACE CLASSES: REDUCED (WORKSHOPS, SEMINARS, CASE STUDIES). As indicated above, this session has a more practical content where teachers can carry out some of the examples given. 100% de presencialidad / A3: STUDENT INDIVIDUAL WORK. 0% de presencialidad / A4: LABORATORY SESSION. This is a series of additional hours where teachers reinforce more practical content with students. 100% de presencialidad / A5: FINAL EXAM. 100% de presencialidad M1: SEMINARS AND LECTURES SUPPORTED BY COMPUTER AND AUDIOVISUAL AIDS. / M2: PRACTICAL LEARNING BASED ON CASES AND PROBLEMS, AND EXERCISE RESOLUTION. / M3: INDIVIDUAL AND GROUP OR COOPERATIVE WORK WITH THE OPTION OF ORAL OR WRITTEN PRESENTATION. / M4: INDIVIDUAL AND GROUP TUTORIALS TO RESOLVE DOUBTS AND QUERIES ABOUT THE SUBJECT.