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Classical Principles of Electromagnetism

Electric ( ) and magnetic field ( ) are caused by electric charges ( e - ) and derive from the same underlying vector field. e. Classical Principles of Electromagnetism. Maxwell Equations s.i . units. Charged particle (charge e , velocity ) in elm field.

JasminFlorian
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Classical Principles of Electromagnetism

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  1. Electric ( ) and magnetic field ( ) are caused by electric charges (e-) and derive from the same underlying vector field e Classical Principles of Electromagnetism Maxwell Equations s.i. units Charged particle (charge e, velocity ) in elm field Int Elm Rad Force F with inertia (m) and initial conditions determine classical trajectory of particle.QM task: Develop theory consistent with measurement

  2. Electric ( ) and magnetic field ( ) are caused by electric charges (e-) and derive from the same underlying vector field e Classical Principles of Electromagnetism Maxwell Equationsc.g.s. units Charged particle (charge e, velocity ) in elm field Int Elm Rad Force F with inertia (m) and initial conditions determine classical trajectory of particle.QM task: Develop theory consistent with measurement

  3. e QM: Charged-Particle Coupling to Elm Field Larger task: Derive an internally consistent quantum mechanical account of the properties of field quanta and interactions with particles. Int Elm Rad

  4. Charged Particles in Elm Fields Explain, or model, Lorentz force on particle (mass m, charge e): Non-conservative, velocity (v) dependent force  effective potential Int Elm Rad

  5. Minimum Coupling to Field Schrödinger Equation for charged (e) particle in elm field Int Elm Rad

  6. 1st Order Interaction Hamiltonian First term is kinetic energy of free, unperturbed particle. Last term is of second order in field A, neglect in first order estimate. Interaction Hamiltonian of particle (mass m, charge q, magnetic moment m) with time dependent elm. field . Add ad hoc spin magnetic interaction Int Elm Rad Make real by adding complex conjugate CC. Larmor frequency.

  7. More Degrees of Freedom Since mp ≈2000·me, electronic terms are dominant for atoms and molecules. Int Elm Rad

  8. Application in Perturbation Theory Interaction Hamiltonian of particle (mass m, charge q, magnetic moment m) with time dependent elm. field . Use in perturbation theory, single-photon emission or absorption Int Elm Rad

  9. Hint with spin and orbital mu Int Elm Rad

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