Editing Appendix/Ramblings/ForCohlHoward (section)

==WKB (geometrical-optics) Method==

As Stephen has pointed out, in {{ LL96b }}, the linearized equations are solved using the "geometrical-optics approximation."  I am not familiar with this so-called "geometrical-optics" method, but in the last couple of paragraphs of &sect;1 of their paper, {{ LL96bhereafter }} refer to it also as the "WKB" approximation/method.  I ''have'' been exposed to this alternate terminology; the WKB approximation has been used by astronomers in connection with efforts to understand the onset and development of "spiral-arm" structures in disk galaxies.  Here is an excerpt from [<b>[[Appendix/References#BT87|<font color="red">BT87</font>]]</b>]. 

<table border="1" align="center" width="80%" cellpadding="8">
<tr><td align="left">
<div align="center">'''The Tight-Winding Approximation'''<br />&sect;6.2.2 (p. 352) of [<b>[[Appendix/References#BT87|<font color="red">BT87</font>]]</b>] </div>
<font color="darkgreen">"&hellip; In the early 1960s a number of workers, notably A. J. Kalnajs, C. C. Lin, and A. Toomre, realized that for tightly wound density waves (''i.e.,'' waves whose radial wavelength is much less than the radius</font> [of the galaxy's disk]) <font color="darkgreen">the long-range coupling</font> [due to gravity] <font color="darkgreen">is negligible, the response is determined locally, and the relevant solutions are analytic.  As we shall see, this '''tight-winding''' or '''WKB approximation'''<sup>&dagger;</sup> is an indispensable tool for understanding the origin and evolution of density waves in galaxies."

----

<sup>&dagger;</sup>Named  after the closely related [https://en.wikipedia.org/wiki/WKB_approximation Wentzel-Kramers-Brillouin approximation] of quantum mechanics.</font>
</td></tr></table>