Know a simple, linear, complex, eigenvalue BVP?

[member 428835]

Hi PF!

I'm trying to find a 1D, linear, complex, 2nd order, eigenvalue BVP: know any that admit analytic solutions? Can't think of any off the top of my head.

Thanks!

 

[jedishrfu]

Would the square well be such a problem?

 

[Haborix]

I take you to mean the function is complex valued over the real line, so it could be written $f=g(x)+ih(x)$. If the differential equation is linear, then wouldn't the problem always reduce to the solving a pair of eigenvalue problems for real functions, $g(x)$ and $h(x)$?

Edit: I also meant to ask if you are looking for a real-world example.

 

[member 428835]

Would the square well be such a problem?

Is this complex? Everything I've checked (here and here) appears to be real.

I take you to mean the function is complex valued over the real line, so it could be written $f=g(x)+ih(x)$.

Sorry, perhaps I did not specify: I mean't so that the eigenvalues/vectors have a real and complex part. Perhaps something like $x''+ix'+x=0$, but I'm at a loss.

Edit: I also meant to ask if you are looking for a real-world example.

Does not need to be a real-world example. I am looking for a good toy problem to work with.