Download Advanced theoretical physics

ADDITIONAL CHAPTER OF THEORETICAL PHYSICS
Educational-Scientific Institute of Gravitation and Cosmology, PFUR
Obligatory course for 5th and 6th course students. Lectures: 48 h., Seminars: 24 h.
Aim
Principled problems of analytical mechanics, Special Relativity, hydro-gaseous
dynamics, microscopic electrodynamics, electrodynamics of continuous media,
quantum mechanics. Course inculuded into the state programme in specialization
«Gravity, cosmology, and relativistic astrophysics».
Theme 1. Analytical mechanics
Least action principle. Lagrange equations. Conservation laws. One-dimensional
motion. Motion in central field. Kepler's laws. Canonical equations, Maupertuis's
principle. Poisson brackets. Hamilton-Jacobi equations. Hamilton-Jacobi method.
Theme 2. Relativistic mechanics
Speed of light absolutism. Interval. Relativity's principle. Lorentz transformations.
Adding of speeds. Simultaneity relativity. Length contraction & time dilatation in a
moving reference system. 4-dimensional vectors. 4-velocity. 4-momentum, 4force. Hyperbolic motion.
Theme 3. Hydro-gaseous dynamics
Perfect fluid. Continuity equation. Euler equation. Viscous fluid. Navier-Stokes
equation. Turbulence. Border-line stratum. Gas motion. Sound. Shock waves.
Relativistic hydrodynamics.
Theme 4. Microscopic electrodynamics
General structure of electrodynamics. Electric charges, electromagnetic field.
Gauge invariance. Maxwell equations. Lorentz force. Relativistic invariance.
Electromagnetic field: Lagrangian, energy-momentum tensor. Charged particle
motion in internal field. Electromagnetic waves. Lienard-Wiechert potentials.
Mulipole expansion. Moments: dipole, quadrupole. Electromagnetic waves
radiation. Larmor formula. Sychrotron radiation. Wave scattering by free charged
particles. Electron's classical radius. Self-interaction force, radiation drag.
Theme 5. Electrodynamics of continuous media
Maxwell equations in medium. Polarization, averaged current density and charge
in medium. Boundary conditions. Dielectrics and conductors: electrostatics. BiotSavart law. Ferromagnetism, superconductivity. Quasistationary electromagnetic
fields. Induction law in running conductors. Skin effect. Electromagnetic waves in
matter. Dispersion. Spread of the waves on the border of two media.
Theme 6. Quantum mechanics
Quantum mechanics: basic formulations, interpretations. Old quantum theory.
Planck formula. Bohr postulates. De Broglie waves. Wave mechanics. KleinGordon equation. Energy and momentum operators. Schrodinger equation. Wave
packet. Uncertainty relations. Commutators. Superposition principle. Wave packet
reduction in measurement process. Ortonormalization conditions of wave
functions. Probabilistic interpretation of wave function. Averaged quantities and
matrix elements of operators. Time derivatives of operators and conservation laws.
Ehrenfest theorem. Harmonic oscillator. Hydrogen atom. Quasiclassical
approximation. Green-Liouville and Wentzel-Kramers-Brillouin methods.
Tunneling effects. Gamov formula. Bohr-Sommerfeld formula. Probability current
denisty. Relativistic quantum mechanics, quantum field theory. Secondary
quantization of bosons and fermions. Bose and Fermi distributions. Dirac equation.
Gamma-matrices. Spin. Quantum theory of radiation. Golden rule of quantum
mechanics. Intensity of dipole electric radiation. Matrix elements of harmonic
oscillator. Oscillator force. Line natural breadth. Einstein-Podolsky-Rosen effect.
Bell inequalities. Hidden symmetries. Quantum teleportation.
Bibliography
Basic
1. L.D. Landau Mechanics (1965)
2. L.D. Landau, E.M. Lifshitz Field theory (1973)
3. L.D. Landau, E.M. Lifshitz Hydrodynamics (1986)
4. L.D. Landau, E.M. Lifshitz Quantum mechanics. Nonrelativistic theory
(1963)
5. V.G. Levich Course of theoretical physics (1969)
6. H. Bethe Quantum mechanics (1965)
Additional
1. V.G. Levich, Yu.A. Vdovin, V.A. Myamlin Theoretical physics course (1971)
2. H. Bethe Quantum mechanics of one- and two- electron atoms (1960)
3. A.S. Davydov Quantum mechanics (1963)
4. V.V. Belokurov, O.D. Timofeevskaya, O.A. Khrustalev Quantum
teleportation – usual miracle (2000)
Composer: M.L. Filchenkov, PhD, Ass. Professor of ESIGC PFUR