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Unformatted text preview: 4.5 Maxwell Equations in Coulomb Gauge 4.5.1 gauge condition => remaining Maxwell Equations (1) (2) special structure: Eqn (1) same as in electrostatics => only one differential equation! insert result into Eqn (2) 4.5.2: Achievability of Coulomb gauge => satisfies Lecture Notes Page 2 5. Vacuum Solutions of Maxwell Eqns. 5.1 Maxwell Equation vacuum => special case of Lorentz gauge possible gauge condition: (also Coulomb gauge!) monochromatic plane waves 5.4 Solution via mode decomposition: 5.4.1 Separation of variables Ansatz whenever continuity will take care of exceptions must be time independent! situations (see below) Note: positive choice would lead to unphysical Time contribution Spatial contribution Helmholtz Equation => each such solution is called a mode => find complete, orthonormal solutions Lecture Notes Page 3...
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- Winter '09
- Lorentz Gauge, Coulomb gauge, Lorentz gauge condition