Fundamentals of Algebra, Differential Equations and Mechanics.

The main objective is to provide an overview of the Schrödinger formulation of Quantum Mechanics. This includes, at a minimum, an introduction to the concept of the wave function, the role of operators in quantum mechanics, and the concept of measurement. The Schrödinger equation is discussed in both one and multiple dimensions, as well as its application to the study of atoms, molecules, and solids. In the case of the latter, band theory is introduced.

Postulates of quantum mechanics.- 1. Wave function. Probabilistic interpretation. 2. Operators and physical magnitudes. Eigenvalues and eigenstates. Space of states. 3. Time evolution of the quantum state. Schrödinger equation. 4. Measurement processes in quantum mechanics. 5. Relation to matrix formulation of QM. Schrödinger equation.- 6. Problems independent of time. Bound and scattering states. Free particles. 7. One-dimensional systems: harmonic oscillator; barrier and wells; quantum tunnelling. 8. Periodic potentials. Bloch theorem. Applications: band theory in solids 9. Kronig-Penney model. Electrons and holes. Metals and insulators. Semiconductors. Superconductivity.