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