Lecture 12 Lecture Notes

Lecture 12 Lecture Notes - Ansatz: each term has to be...

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monochromatic plane waves 5.2 Solution via mode decomposition: 5.2.1 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 5.2.2 Time contribution for some => seek real solutions: conditions on => for some Note: choice would have led to for large : exponential growth => unphysical! => leads to exponential growth of energy densities etc Lec 12 - 30. Jan January 29 09 9:54 PM Lecture Notes Page 1
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5.2.3 Spatial contribution Helmholtz Equation
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Unformatted text preview: Ansatz: each term has to be independent of all variables!-choice of positive constant leads to unphysical situations again-=> as before real valued solutions such that same for sum over all satisfying 5.2.5 New elementary solution Lecture Notes Page 2 5.2.6 Complete mathematical solution (up to diverging solutions) These solutions are 'monochromatic transversal plane waves' ! 5.2.7 gauge condition: restricting to physical solutions for any two choices! => polarization with Function of Lecture Notes Page 3...
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This note was uploaded on 07/28/2009 for the course PHYS 441B taught by Professor Norbertlutkenhaus during the Winter '09 term at Waterloo.

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Lecture 12 Lecture Notes - Ansatz: each term has to be...

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