SOLID STATE PHYSICS

The course is one of the free-choice educational activities of the Bachelor of Science in Engineering Physics and enables the student to understand the fundamental physical theories that have been developed to describe the behaviour of "condensed matter", i.e., the materials that are commonly called "solids".

The course intends to provide an understanding on how physical theories that are based on classical and quantum statistical mechanics, through relatively simple assumptions, can provide qualitative insight into the general behaviour and the peculiar properties of solids, i.e., their ability to transport heat and charge.

At the end of the lectures, the students will know the basic theories that are used to describe the transport of heat, pressure (acoustic waves) and charge (electric current) in solid materials.

The students are expected to know and understand the theories exposed during the lectures, and to be able to use those theories to gain insight into the physical behaviour of solids.

The course does not formally require having passed previous courses, but takes for granted many of the concepts covered in the courses of Mathematical Analysis 1 and 2 (derivatives and integrals to one and more variables), Linear Algebra (vector spaces and operations between vectors, equations to eigenvalues), Mathematical Methods for Physics and Engineering (Hamiltonian formalism), Physics 1 (classical harmonic motion), Quantum Mechanics (quantum harmonic oscillator).

THEORY OF MEDALS: Atomic models for metals; Drude's model; Electrical conductivity; Thermal Conductivity and Wiedman-Franz law; Sommerfield's model; Electron gas and Fermi sphere; Pressure of Fermi gas; Density of states; Metals at finite temperatures and specific heat; Conductivity in Sommerfeld's theory.

INTRODUCTION TO CRYSTAL STRUCTURES: Limitations of the free-electron model; Bravais lattices; Reciprocal lattices; Examples of Bravais and reciprocal lattices for simple crystalline structures.

BAND THEORY: Bloch's theorem; Born-Von Karman periodic boundary conditions; Tight binding theory; Quasi-free electron theory; Band gap and Brillouin zones; Bragg's scattering and Bragg's planes.

CLASSICAL THEORY OF HARMONIC CRYSTALS: Classical equipartition function and Doulong-Petit theory; One-dimensional crystals and harmonic approximation; Normal modesl of a biatomic molecule; Normal modes of a harmonic crystal.

QUANTUM THOERY OF HARMONIC CRYSTALS: Quantum theory of harmonic oscillators; Einstein's theory of specific heat in solids; Debye's theory of specific heat in solids; Debye's temperature and Debye's wavevector and their physical interpretation.

Ashcroft & Mermin, "Solid State Physics"

The student's knowledge of the materials treated during the lectures will be assesed through an oral examination. The students are expected to show, during the final exam, their mastery of the subject matter and also the ability to explain it formally. The oral examination will tipically last between 20 and 30 minutes, and it will involve two or tree questions regarding the course's contents. The studends will have to show their understanding of the materials taught in the course by answering, using the board if necessary. The formal and mathematical abilities and the physical insight are considered equally important.

A completely satisfactory exam (mark: 27-30) will envolve a good mastery of the material presented during the lectures. A medium mark (22-26) will be given if the understanding acquired is failry complete, but limited connections between the different arguements covered in the course has been acquired. Finally, a passing mark (18-21) will be given if a minimal knowledge has been acquired.

The course will be given in classroom lectures.

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