What wave function should I choose for this problem?

[rwooduk]

Homework Statement

Show that the operator

$$O = i\frac{d^{3}}{dx^{3}}$$

has real eigenvalues

Homework Equations

Differentiate a wave function 3 times

The Attempt at a Solution

I know the process of differentiating a wave function (as many times as you like) and it giving the wave function back multiplied the eigen value. But this question seems so general, what wave function should I choose?

thanks in advance for any pointers

 

[hilbert2]

The eigenfunctions are linear combinations of functions of form $e^{kx}$. To give an ansver to the problem, you should explain why $k$ has to be imaginary for this to be an acceptable wave function (if k were real, the eigenvalue would be imaginary).

 

[rwooduk]

The eigenfunctions are linear combinations of functions of form $e^{kx}$. To give an ansver to the problem, you should explain why $k$ has to be imaginary for this to be an acceptable wave function (if k were real, the eigenvalue would be imaginary).

that's very helpful, thank you!