Are there any other popular eigenfunctions other than e^x, sinx, cosx, and combinations of those? And before you say sinx isn't an eigenfunction, it is an eigenfunction of the second derivative operator.

Question

anonymous · Answer

I don't believe so. I'm guessing a function that is constantly zero doesn't count...

kainui · Answer

Wow, I did some looking and found some really simple ways to make eigenfunctions. It's really all in the operator. For instance:

$$x \frac{ d }{ dx }(x^n)=nx^n$$

So you can pretty simply see that x^n is an eigenfunction of the x*d/dx operator. Kind of silly to see now that it's obvious.

So for instance (lol) $$tan(ax )*\frac{ d }{ dx }[sin(ax)]=asin(ax)$$ and now sin(ax) is an eigenfunction. Bleh. But is it useful for anything?

anonymous · Answer

isn't that sort of cheating?