Question

What is the eigen value when the eigen function e^ax is operated on the operator d^n/dx^n ?
(A) a^-n
(B) a^n
(C) a^-xn
(D) na^ax​

Answer 1

Answer:

I'm gradually getting familiar with operators (as they are used in QM) and the terminology surrounding them, and I was wondering whether all the (to me) well-known operators have straight-forward, elementary functions, as seems to be the case with d(n)dx, because

d(n)dxeax=aneax

and could one say that the spectrum of these eigenfunctions is degenerate, since a can vary (I know "spectrum" is usually used for the set of eigenvalues, but it seems appropriate here)? Is this the correct interpretation? If so, what is the eigenfunctions and -values for the following differentialoperators (if you could point me in the direction of a resource that either collects them or - even better - shows how they are obtained, that would be very acceptable):

∫dx

∇ (grad)

∇⋅ (div)

∇2 (Laplace)

If you have a cool one, please do just throw it in there!

Thanks!

Explanation:

hope it help you pls make me brainliest thanks