Understanding Classical Mechanics and Fields in Physics

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Explore the concepts of radiation, matter, fields, Hamiltonian, and more in classical mechanics with a focus on velocity-dependent potentials and conservative systems. Dive into the detailed discussions on gauge theory, Coulomb gauge, magnetic fields, and Hamiltonian operators within the framework of physics.


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  1. 1.RADIATION J. Planelles

  2. 2.Matter and Field J. Planelles

  3. Classical Mechanics: an overview Newton s Law Conservative systems Lagrange equation

  4. Velocity-dependent potentials Time-independent field No magnetic monopoles

  5. Velocity-dependent potentials: cont. Define:

  6. Velocity-dependent potentials: cont. kinematic momentum: canonical momentum: Hamiltonian:

  7. Conservative systems: V(x,y,z) & L = T - V canonical momentum: kinematic momentum: Hamiltonian:

  8. Gauge ; We may select : Coulomb Gauge :

  9. Hamiltonian (coulomb gauge) ;

  10. Magnetic field: summary No magnetic monopoles: vector potential velocity-dependent potential: No conservative field: Lagrangian: kinematic momentum Canonical momentum: Hamiltonian: Coulomb gauge: Hamiltonian operator:

  11. 3. Electron-photon interaction (selection rules and resonanace) J. Planelles

  12. Hamiltonian of a charge in an electromagnetic field Set of charges {qi}:

  13. Time-dependent perturbation theory

  14. Time-dependent perturbation theory (cont.) Transition probability: Taylor expansion:

  15. Time-dependent perturbation theory (cont.)

  16. Time-dependent perturbation theory (cont.) resonance: resonance: selection rule:

  17. Time-dependent perturbation theory (cont.) First (and larger) perturbation term: (with q = - e, m of electron) Integral involved: Single photon transition Spontaneous emission

  18. Time-dependent perturbation theory (cont.) After some algebra:

  19. Time-dependent perturbation theory (cont.) Second (smaller) perturbation term: (q = - e, m of electron) terms : two-photon transitions two-photon transitions: weak ( use LASER). e.g. Raman

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