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

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EELT7025 - Methods / ECMA7043 – Topics

Quantum Mechanics With Applications

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