# 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

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
hilbert2 said:
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).