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Curriculum framework

  1. The Master’s Program in Physics at PGF has a curriculum structure aligned with the diverse nature of its research lines. Student performance is evaluated throughout the program based on the following criteria:
  • Courses: Divided into mandatory and elective subjects;
  • Credit-bearing activities: Guided Study and Dissertation;
  • Non-credit-bearing activities: Dissertation Plan Monitoring, Foreign Language Proficiency, and Teaching Internship;
  1. To complete the program, students must earn 24 credits through courses and activities, with one (1) credit corresponding to 15 hours of class time.
  2. Students may take only one Guided Study, which will count for the same number of credits as a regular course of equivalent workload.
  3. Dissertation Plan Monitoring is a mandatory activity and must be enrolled in every academic term.
  4. Students must submit their Dissertation Work Plan to the PRPPG office using the designated form within six (6) months of their initial enrollment.
  5. All students in the program must demonstrate English language proficiency at a B1 level, as classified by the Common European Framework of Reference for Languages (CEFR).
  6. The Teaching Internship is a mandatory requirement for scholarship holders.
  7. For more information, please refer to the Program Regulations and the UNIFEI Graduate Program Guidelines.

Mandatory Courses:

  1. Difficulties of classical theory in describing microscopic physical phenomena;
  2. Schrödinger equation;
  3. Mathematical tools of Quantum Mechanics;
  4. Quantum Dynamics;
  5. Symmetries and Conservation Laws;
  6. Rotations and Angular Momentum;
  7. Hydrogen-like Atoms.
Bibliography:

–  J.J. Sakurai and J. Napolitano. Modern Quantum Mechanics. Cambridge University Press. Second edition (2017).
–  C. Cohen-Tannoudji, B. Diu, and F. Laloë, Quantum Mechanics, vol 1. Wiley. New York (1991)

Optional subjects in astrophysics:

  1. Physical properties of stars
  2. Physical conditions in stellar interiors
  3. Electron gas
  4. Photon gas
  5. Polytropic stars
  6. Opacity
  7. Convection
  8. Thermonuclear reactions
  9. Energy production
  10. Stellar structure calculations
  11. Stellar evolution
Bibliography:

–  Kippenhahn, R., & Weigert, A., Stellar Structure and Evolution, Springer-Verlag, Berlin, 1994.
– Maciel, W.J., Introdução à Estrutura e Evolução Estelar, Edusp, São Paulo, 1999.
– Cox, A., Astrophysical Quantities, Springer-Verlag, Berlin, 2000.
– Clayton, D.D., Principles of Stellar Evolution and Nucleosynthesis, University of Chicago Press, Chicago, 1984.

  1. Historical background and our galaxy
  2. Galaxy classification
  3. Properties: luminosity, colors, spectra, elliptical galaxies
  4. Spiral galaxies
  5. Star formation in galaxies
  6. Active Galactic Nuclei (AGNs)
  7. Distance scales
  8. Local galaxy distribution
  9. Galaxy groups and clusters
  10. Large-scale structure
  11. Foundations of cosmology
Bibliography:

– Combes, F., Boissé, P., Mazure, A., & Blanchard, A., Galaxies and Cosmology, Springer-Verlag, Berlin, 2004.
– Binney, J., & Tremaine, S., Galactic Dynamics, Princeton Series in Astrophysics, 1987.
– Schneider, P., Extragalactic Astronomy and Cosmology: An Introduction, Springer, 2009.

  1. Basic concepts
  2. Closed-box model
  3. Stellar abundances
  4. Stellar yields and evolution concepts
  5. Stellar mean lifetimes and element production
  6. Initial Mass Function: estimates, theoretical models, and applied functions
  7. Analytical classical models
  8. Numerical models
  9. MULCHEM code
  10. Stellar populations and evolutionary synthesis models
  11. Cosmological simulations
Bibliography:

– Lynden-Bell, D., & Fall, M. (Eds.), The Structure and Evolution of Normal Galaxies, Cambridge University Press, 1979.
– Tinsley, B.M., Evolution of Stars and Gas in Galaxies, 1980.
– Pagel, B.E.J., Nucleosynthesis and Chemical Evolution of Galaxies, Cambridge University Press, 1997.
– Matteucci, F., Chemical Evolution of Galaxies, Springer, 2012.
– Astronomy and Astrophysics Library, Springer-Verlag, Berlin Heidelberg.

  1. Observational foundations of modern cosmology
  2. Thermal history of the universe
  3. The primordial universe
  4. Cosmic Microwave Background Radiation (CMB)
  5. Dark Matter
  6. Large-scale structure formation
  7. The Standard Cosmological Model
Bibliography:

– Lima Neto, G.B., Astronomia Extragaláctica e Cosmologia, 2020
– Ryden, B., Introduction to Cosmology, 2nd edition.

  1. Galaxy components
  2. Stellar statistics
  3. Stellar and galactic evolution
  4. Stellar kinematics
  5. Stellar dynamics
  6. Galaxy systems
Bibliography:
  1. Interstellar radiation field
  2. Heating and cooling processes
  3. Gaseous component: density, temperatures, and interstellar lines
  4. Solid component
  5. Galactic magnetic field
  6. Dynamic processes
  7. Star formation and matter exchange
Bibliography:
  1. Numerical solutions of first-order differential equations
  2. Numerical solutions of Newton’s equations of motion
  3. Planetary orbit simulations and verification of Kepler’s laws
  4. Numerical solutions of Laplace and Poisson equations
  5. Monte Carlo simulations of random walks
  6. Qualitative study of special functions
  7. Numerical integration
Bibliography:

– Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P., Numerical Recipes 3rd Edition: The Art of Scientific Computing, Cambridge University Press, 2007.
– Gould, H., & Tobochnik, J., Computer Simulation Methods – Applications to Physical Systems, Parts 1 and 2, Addison-Wesley Publishing Co., 1988..
– Wolfram, S., The Mathematica Book, 5th ed., Wolfram Media, 2003.

  1. Ionization structure
  2. Nebular emission lines
  3. Nebular continuum emission
  4. The neutral gas component
  5. The dust component
  6. Observations of central stars
  7. Morphologies
  8. Progenitors of nebulae
  9. Evolution of central stars
  10. Formation and evolution of nebulae
  11. Chemical abundances
  12. Nebulae in other galaxies
Bibliography:
  1. Radiative transfer
  2. Photon emission and absorption mechanisms
  3. Radiation from moving charges
  4. Special relativity effects
  5. Bremsstrahlung and synchrotron radiation
  6. Inverse Compton radiation
  7. Plasma effects
  8. Atomic structure
  9. Radiative transitions
  10. Molecular levels
  11. Astrophysical applications
Bibliography:
  1. CCD device functioning
  2. Essential techniques
  3. Data pre-processing
  4. Data processing techniques in PSF photometry
  5. Data processing techniques in spectroscopy
  6. Software for optical data reduction in astrophysics
Bibliography:

High-Energy Observational Techniques:
1.1. Interactions of high-energy photons
1.2. Detectors for high-energy particles, X-rays, and gamma rays
1.3. Cosmic ray, X-ray, gamma-ray, and neutrino telescopes
1.4. Technical visit: National Institute for Space Research (INPE)
1.5. Data reduction and analysis

Ultraviolet, Visible, and Infrared Observational Techniques:
2.1. Photometry
2.2. Spectroscopy
2.3. Detectors
2.4. Technical visit: Pico dos Dias Observatory
2.5. Data reduction and analysis

Radio Astronomy Observational Techniques:
3.1. Basics of radio astronomy: fundamental concepts, radiative processes, and atmosphere
3.2. Radio telescopes: sensitivity, resolution, antennas, receivers, spectrometers, and interferometers
3.3. Practical radio astronomy: characterization, observational methods, and VLBI
3.4. Technical visit: National Institute for Space Research (INPE)
3.5. Data reduction and analysis

Bibliography:

– Longair, M.S., High Energy Astrophysics, 2nd edition, Cambridge University Press, 1992.
– Smith, R.C., Observational Astrophysics, Cambridge University Press, 1995.
– Léna, P., Observational Astrophysics, Springer-Verlag, 1988.

Specific astrophysical topics not covered in the program’s standard courses.

Optional subjects for physics:

  1. The hot universe
  2. Homogeneous inflation
  3. Newtonian gravitational instability
  4. Relativistic gravitational instability
  5. Primordial inhomogeneities and inflation
  6. Cosmic microwave background anisotropies
  7. Distance scales
  8. Local galaxy distribution
  9. Galaxy groups and clusters
  10. Large-scale structure
  11. Foundations of cosmology

Bibliography:

– Mukhanov, V.F., Physical Foundations of Cosmology, Cambridge University Press, 2008.

– Narlikar, J.V., An Introduction to Cosmology, Cambridge University Press, 2002.


This course will cover the concepts of X-ray diffraction and its application in characterizing ordered materials (crystalline and polycrystalline). It will also introduce the concepts of X-ray reflection and its application in characterizing thin films. The technical characteristics of a conventional high-resolution X-ray diffractometer and the XRD-2 beamline at the National Synchrotron Light Laboratory (LNLS) will be presented, along with their application potential for characterizing various materials. Topics related to the use of X-ray diffraction and reflection techniques for specific material characterization will also be covered.

Bibliography:

– Ashcroft, N.W., & Mermin, N.D., Solid State Physics, Chapters 4, 5, and 6.

– Kittel, C., Introduction to Solid State Physics, Chapters 1 and 2.

– Cullity, B.D., Elements of X-ray Diffraction.

  1. Review of modern physics
  2. Free electrons in metals
  3. Sommerfeld’s theory of metals
  4. Crystal lattices
  5. Reciprocal lattice
  6. Determination of crystal structure by X-ray diffraction
  7. Electrons in a periodic potential
  8. Superconductors

Bibliography:

– Kittel, C., Introduction to Solid State Physics, 8th ed., Wiley, 2004.

– Ashcroft, N.W., & Mermin, N.D., Solid State Physics, Cengage Learning, 1976.

  1. Review of modern physics
  2. Free electrons in metals
  3. Sommerfeld’s theory of metals
  4. Crystal lattices
  5. Reciprocal lattice
  6. Determination of crystal structure by X-ray diffraction
  7. Electrons in a periodic potential
  8. Superconductors
Bibliography:

– Kittel, C., Introduction to Solid State Physics, 8th ed., Wiley, 2004.
– Ashcroft, N.W., & Mermin, N.D., Solid State Physics, Cengage Learning, 1976.

  1. Fermi surfaces
  2. Nanostructures
  3. Point defects
  4. Alloys
  5. Phonons in metals
  6. Homogeneous semiconductors
  7. Inhomogeneous semiconductors
  8. Electronic interactions and magnetic structure

Bibliography:

– Kittel, C., Introduction to Solid State Physics, 8th ed., Wiley, 2004.

– Ashcroft, N.W., & Mermin, N.D., Solid State Physics, Cengage Learning, 1976.

  1. Introduction
  2. Heaviside functions and Dirac delta function
  3. Fourier series and integral
  4. Non-relativistic vibrating string
  5. Review of special relativity and tensors
  6. Electromagnetism and gravitation in multiple dimensions
  7. Classical field theory in coordinate system and light-cone gauge
  8. Relativistic particles
  9. Classical relativistic string (non-quantum)
  10. Free field quantization
  11. Quantum relativistic particle
  12. Lorentz algebra
  13. Quantum relativistic open string

Bibliography:

– Zwiebach, B., A First Course in String Theory, 2nd edition, Cambridge University Press, 2009.

  1. Materials for electronics
  2. Electrons in crystals
  3. Semiconductor materials
  4. Semiconductor devices
  5. Optoelectronic materials and devices
  6. Quantum theory of radiation-matter interaction

Bibliography:

– Rezende, S.M., Materiais e Dispositivos Eletrônicos, Editora Livraria da Física, 2004.

– Kittel, C., Introduction to Solid State Physics, 7th ed., John Wiley & Sons, 1996.

– Wolfe, C.M., Holonyak, N. Jr., & Stillman, G.E., Physical Properties of Semiconductors, Prentice Hall, 1989.

– Sze, S.M., Physics of Semiconductor Devices, John Wiley & Sons, 1981.

– Look, D.C., Electrical Characterization of GaAs Materials and Devices, John Wiley & Sons, 1989.

  1. Equations of motion
  2. Conservation laws
  3. Integration of motion equations
  4. Collisions
  5. Small oscillations
  6. Oscillations of multi-degree-of-freedom systems
  7. Rigid body motion
  8. Canonical equations

Bibliography:

– Landau, L., & Lifshitz, L., Mechanics, Pergamon Press, 1960.

– Goldstein, H., Classical Mechanics, Addison-Wesley, 1950.

– Lanczos, C., The Variational Principles of Mechanics, Dover Publications, 1986.

– Fierz, M., Mecánica General, Editorial Trillas, 1977.

  1. Thermodynamics
  2. Kinetic theory of gases
  3. Classical statistical mechanics
  4. Quantum statistical mechanics

Bibliography:

– Huang, K., Statistical Mechanics, John Wiley & Sons, 1987.

– Pathria, R.K., Statistical Mechanics, Pergamon Press, 1972.

– Landau, L.D., & Lifshitz, E.M., Course of Theoretical Physics, Vol. 5: Statistical Physics, Pergamon Press, 1963.

  1. External gravitational field
  2. Gravitational dynamics
  3. Field of gravitating bodies
  4. Gravitational waves
  5. Relativistic cosmology

Bibliography:

– Adler, R., Bazin, M., & Schiffer, M., Introduction to General Relativity, 2nd ed., McGraw-Hill, 1975.

– Weinberg, S., Gravitation and Cosmology – Principles and Applications of the General Theory of Relativity, Wiley, 1972.

  1. DC measurements
  2. Impurity bands
  3. AC measurements
  4. Support equipment
  5. Control and data acquisition programs
  6. Power supplies, multimeters, source/measurement units, electrometers
  7. Furnaces and cryostats with temperature control
  8. Atmosphere and vacuum control
  9. I(V) measurements
  10. Resistivity (T)
  11. Hall effect and magnetoresistance
  12. Impedance spectroscopy

Bibliography:

– Rezende, S.M., Materiais e Dispositivos Eletrônicos, Editora Livraria da Física, 2004.

– Kittel, C., Introduction to Solid State Physics, 7th ed., John Wiley & Sons, 1996.

– Wolfe, C.M., Holonyak, N. Jr., & Stillman, G.E., Physical Properties of Semiconductors, Prentice Hall, 1989.

– Shklovskii, B.I., & Efros, A.L., Electronic Properties of Doped Semiconductors, Springer-Verlag, 1984.

– Keithley, Low Level Measurements, Keithley Instruments, 1984.

– Tsao, J.Y., Material Fundamentals of Molecular Beam Epitaxy, Academic Press, 1993.

– Sze, S.M., Physics of Semiconductor Devices, John Wiley & Sons, 1981

– Look, D.C., Electrical Characterization of GaAs Materials and Devices, John Wiley & Sons, 1989.

  1. Relativistic mechanics
  2. Electromagnetic field
  3. Electromagnetic waves
  4. Electromagnetic radiation
  5. Electromagnetism in material media
  6. Radiation in material media

Bibliography:

– Landau, L.D., & Lifshitz, E.M., The Classical Theory of Fields, Vol. 2, 3rd ed., 1987.

– Jackson, J.D., Classical Electrodynamics, 3rd ed., John Wiley & Sons, 1998.

  1. Approximate methods
  2. Identical particles
  3. Scattering theory
  4. Bell’s theorem

Bibliography:

– Sakurai, J.J., & Napolitano, J.J., Modern Quantum Mechanics, Addison-Wesley, 2010.

– Weinberg, S., Lectures on Quantum Mechanics, Cambridge University Press, 2012.

  1. Particles and fundamental interactions
  2. Lagrangian formulation and symmetries; Noether’s theorem
  3. Canonical quantization and particle interpretation
  4. Quantum field theory in the path integral formalism
  5. Spin 0: scalar fields
  6. Spin 1/2: spinor fields
  7. Spin 1: vector fields

Bibliography:

– Srednicki, M., Quantum Field Theory, 1st ed., Cambridge University Press, 2007.

– Peskin, M.E., & Schroeder, D.V., An Introduction to Quantum Field Theory, 2nd ed., CRC Press, 2007.

– Weinberg, S., The Quantum Theory of Fields, Vol. 1, 1st ed., Cambridge University Press, 2005.

– Zee, A., Quantum Field Theory in a Nutshell, Princeton University Press, 2003.

– Ryder, L.H., Quantum Field Theory, Cambridge University Press, 1996.

  1. Functional methods in quantum field theory
  2. Renormalization
  3. Non-Abelian gauge fields
  4. Renormalization of gauge theories
  5. Massive gauge fields
  6. Gauge theory of gravitation
  7. Quantum fields in curved spaces

Bibliography:

– Zuber, J.-B., & Itzykson, C., Quantum Field Theory, 1st ed.

– Peskin, M.E., & Schroeder, D.V., An Introduction to Quantum Field Theory, 2nd ed., CRC Press, 2007.

– Weinberg, S., The Quantum Theory of Fields, Vol. 2, 1st ed., Cambridge University Press, 2005.

– Zee, A., Quantum Field Theory in a Nutshell, Princeton University Press, 2003.

– Ryder, L.H., Quantum Field Theory, Cambridge University Press, 1996.

Topics on specific subjects in theoretical physics that are not covered in the regular course curriculum.

About

  • Degree: Master
  • Capes' Rating: grade 4
  • Duration: 360 hours
  • Campus: Itajuba

Coordination

COORDINATOR

Alexis Roa Aguirre

alexis.roaaguirre@unifei.edu.br

ASSISTANT COORDINATOR

Eduardo Henrique Silva Bittencourt

bittencourt@unifei.edu.br

Program Committee

  • Prof. Alexis Roa Aguirre
  • Prof. Danilo Roque Huanca
  • Prof. Marcelos Lima Peres
  • Guilherme Roberto Tavares

Secretary

  • Gabriel Viana Rennó de Oliveira
  • In-person service:: Monday to Friday
  • Office hours: from 8h to 12am and 2h to 5pm
  • E-mail: prppg.ifq@unifei.edu.br
  • Phone: +55 (35) 3629-1843
Copyright © 2025 PGF | Developed by IT staff of PRPPG
  • Av. BPS, 13001 - Pinheirinho, Itajubá - MG
  • PO Box 50 ZIP Code: 37500 903
  • Phone: +55 (35) 3629 – 1101
  • E-mail: prppg.ifq@unifei.edu.br
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