The present course was delivered in English in the 1st. semestre of the academic year 2020, for MSc and PhD students in the Graduate Programs of Electrical Engineering (PPGEE/UFPR) and Materials Science and Engineering (PIPE/UFPR).
Hour Load: 60h / 04 Credits
Syllabus: Particles and Classical Fields, Hilbert Spaces, Postulates of Quantum Mechanics, 1st Quantization, Spin ½ Systems and Magnetic Resonance, Canonical Field Quantization or 2nd Quantization, Bosonic and Fermionic Operators, Quantum Statistics, Elementary Excitations in Condensed Matter: phonons, magnons and excitons, Linear Response and Kubo Theory, Metals, Semiconductors, Light-Matter interactions and Laser, Tight-binding models, Quantum transport, Magnetic properties of matter.
Textbooks:
-J.J. Sakurai, Modern Quantum Mechanics (Revised Edition)
-C. Kittel, Quantum Theory of Solids (John Wiley & Sons, New York)
-W. Greiner, J. Reinhardt, Field Quantization(Springer-Verlag Berlin)
-A. Altland, B. Simons, Condensed Matter Field Theory (Cambridge Press)
-O. Madelung, Introduction to Solid State Theory (Springer-Verlag Berlin)
-Robert M. White,Quantum Theory of Magnetism (Springer-Verlag, Berlin, 1983);
The lectures are available online at YouTube:
0 - Particles and Fields
1 - Hilbert Spaces
2 - Representations:and Basis Transformations
3 - Fourier Transforms
4 - Postulates of QM Part 1
5 - Postulates of QM Part 2 Uncertainty Relations
6 - Averages, Measurements...
7 - Momentum and Position Spaces
8 - Pauli Matrices, More on Basis Transformations
9 - Brief Review of Gaussian Integrals
10 - Hamiltonian Formalism in Classical Mechanics
11 - Quantum Dynamics: Schrodinger's Equation and Heisenberg
12 - Differential Operators as Matrices
13 - Spin 1/2 Systems: Pauli Matrices and Rotations
14 - Quantum Dynamics of Spin 1/2 System: Spin Precession
15 - Two-level Systems: Mapping to a Spin 1/2 Problem
16 - Two-Level Systems: Rabi Oscillations
17 - Quantum Evolution of a Gaussian Wavepacket
18 - The Infinite Square Well
19 - Harmonic Oscillator and Ladder Operators
20 - Some Comments on Numerical Methods: Eigenvalues and Eigenvectors
21 - Some Comments on Numerical Methods: Time Evolution
22 - Asymmetric Potential Well, Double Well and Tunnelling
23 - Basic Aspects of Group Theory
24 - Lie Groups, Rotation Group and its Representations
25 - Spin-Statistics Theorem: Bosons and Fermions
26 - Number Representation, Bosonic and Fermionic Algebras
27 - A Recipe for Field Quantization (or 2nd Quantization)
28 - What are the Field Operators?
29- The Hamiltonian in Second Quantization: Non-interacting and Interacting Terms
30 - Coulomb Interactions in Second Quantized Version
31 - Density Operator Formalism and The Magnetic Susceptibility of a Spin 1/2 System
32 - Bose-Einstein and Fermi-Dirac Statistics
33- Density of states
34- Fermi Gas - Part 1
35– Fermi Gas - Part 2
36- Bose Gas: Phonons, Photons and Magnons
37- Bose Gas: The Debye model of specific heat in solids
38- Photon Gas and Blackbody Radiation
39 -Tight-binding models, Energy bands, Semiconductors, Hubbard models