Physics
The graduate of the doctoral study of theoretical physics (hereinafter referred to as "graduate") masters the extensive mathematical apparatus and theoreticalphysical methods for solving complex problems in systems composed of interacting subparts. The application of the mathematical apparatus and these scientific methods is not limited to physical systems, but to all areas of human activity, the structure of which cannot be understood by direct sensory perception, but only by theoretical abstractions.
Theoretical knowledge:
The graduate can work scientifically and provide original solutions to complex problems in the following areas:
 General and mathematical physics,
 Quantum field theory,
 Condensed matter theory,
 Subnuclear physics,
 In original applications of the methods of mathematical and theoretical physics to other scientific disciplines.
Additional knowledge and skills:
In addition to theoretical knowledge, the graduate will acquire:
 methods of scientific work, i.e. identification and prediction of new phenomena,
 analysis, description and explanation of phenomena that are not fully understood,
 implication of new phenomena in broader contexts to their eventual technological application,
 use of sophisticated numerical and analyticalnumerical procedures to solve problems that have no analytical solutions,
 presentation of the achieved scientific results in professional journals and monographs as well as at international conferences.
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successful completion of the entrance exam
Additional information
Astrophysics
Equation of state of stellar matter, excitation, Boltzmann equation, ionization, Sah equation. Stellar structure, hydrostatic and radiative equilibrium, energy transfer by radiation, conduction and convection. Energy transfer in the atmosphere of stars. Radiative transfer equation. Origin of the spectrum and basic properties. Basic equations of stellar structure and their solution. Sources of energy in stars. Formation and evolution of stars. Final stages of stellar evolution, degenerate star model, white dwarfs, neutron stars, pulsars, black holes. Variable stars and their subdivisions , causes of variability, basic types of variable stars
Principle of geometrical optics, optical errors and their correction, types of telescopes their construction, radio telescopes, satellite UV and X telescopes, light detectors: CCD, CMOS, basics of photometry, spectroscopy and polarimetry
Nuclear and subnuclear physics
The admission interviews will require knowledge within the scope of the state final examination in the field of nuclear and subnuclear physics.
Theoretical Physics
Mathematical and computational physics:Complex variable, analytic functions, Cauchy integral theorems, theory of residues. Differential equations, second order ordinary differential equations with constant coefficients, Euler's equation. Euler's method of solving differential equations by separation of variables. SturmLiouville problem, boundary conditions and problems. Bessel functions, Legendre, Laguerre and Hermite polynomials. Solution of the Laplace equation in spherical coordinates, spherical functions. Classification of second order differential equations, characteristic equation. Numerical solution of systems of algebraic equations, construction of numerical quadratures for systems of differential equations and partial differential equations. Classification of dynamical systems using invariant measures, identification of chaos. Discrete Fourier transform. Monte Carlo method, generation of partition functions in statistical physics ensembles, applications in magnetism theory. Method of molecular dynamics. Stochastic differential equations. Modelling based on cellular automata and autonomous agents. Functionally stable partition functions. Optimization methods.
Theoretical physics: Basic principles of classical mechanics: the principle of virtual works, d'Alembert's principle and Hamilton's principle. Lagrange's and Hamilton's canonical equations. Principle of relativity, Lorentz transformation, proper time, interval in fourdimensional space, fourvector momentum, relativistic equations of motion. System of Maxwell's equations in vacuum and in matter. Electromagnetic field potentials. Calibration invariance. Fourdimensional current density vector and fourdimensional potential. System of Maxwell's equations in vacuum in covariant form, electromagnetic field tensor. Electrostatic field, stationary magnetic field and quasistationary electromagnetic field. Electromagnetic waves. Plane monochromatic wave and its polarization. Basic concepts of quantum mechanics: uncertainty principle, superposition principle, states and quantities in quantum mechanics, operators of basic physical quantities. Schrödinger equation, Hamiltonian. Simple quantum mechanical systems: particle in potential cavity, particle passing through potential barrier, harmonic oscillator, hydrogen atom. Spin, Pauli exclusion principle. Statistical ensembles and distributions. Microcanonical, canonical and grand canonical distributions in classical and quantum statistical physics. Boltzmann, BoseEinstein and FermiDirac distributions. Quasiparticles in solids, phonons and magnons. Specific heat. Phase transitions, classification of phase transitions. Landau's theory of phase transitions.
oral

Apply the application for study
01.03.2024  31.05.2024

Performance of the entrance exam
17.06.2024  28.06.2024
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 CV
 verified copy of the degree for applicant of other universities
 photocopy of the Diploma Supplement to candidates from other universities
Annual tuition fees
Standard length of study: cost free
The fee for admission procedure
application form: 50 €
Eapplication form: 40 €
Billing information
Bank: Treasury. Bank code: 8180
Account number: SK 28 8180 0000 0070 0007 8491
Variable symbol: 2996
Constant symbol: 0308
Specific symbol: birth number without slash
Recipient message: name and surname of the applicant
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We will send you all the information about important events and deadlines.
Responsibility for content: RNDr. Iveta Sováková – iveta.sovakova@upjs.sk
Last update: 30.11.2023 09:39