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## Homework Statement

Here is a photo of a page in Laser Physics by Hooker:

https://www.evernote.com/shard/s245/sh/2172a4e7-63c7-41a0-a0e7-b1d68ac739fc/7ba12c241f76a317a6dc3f2d6220027a/res/642710b5-9610-4b5b-aef4-c7958297e34d/Snapshot_1.jpg?resizeSmall&width=832

I have 3 questions (I'm a bit rusty after a long summer):

1. Is the "c.c." bascially [itex]\textbf{U}(r) e^{i \omega t}[/itex] or is the

**U**actually

**U***? (Just checking)

2. Why can't we say [itex] \textbf{U}(r) = X(x)Y(y)Z(z) [/itex] instead of separating it into Ux Uy and Uz?

3. Finally: Having gone through the PDE and got an answer with boundary solutions [itex]\textbf{U}(r)_{x} = 0[/itex] at edges, I don't understand where the [itex]\frac{\pi}{L}[/itex] comes from. The π I know is just put into make the mode numbers simpler later, but how does the L get there?

And how is the x component a cos function? I get a sin!

Thanks for the help! I'm just a bit rusty!