Potential Step where E>V0. λ(II) always twice λ?

[ZedCar]

Homework Statement

I have been attempting some questions on a particle approaching a potential step where

E>V0

I have the provided solutions for all the questions and I noticed that λ(II) is always twice the value of λ in all the questions.

Is there some inherent reason for this, and is it always the case with this type of problem?

Thank you.

Homework Equations

The Attempt at a Solution

 

[Simon Bridge]

What type of problem?

Assuming I and II are the regions before and after the step respectively, and λ is a characteristic wavelength of the wavefunction, so that k=2π/λ

If E >> V, the height of the step, then there should be almost no difference.
If E ~ V, then there should be some reflection off the edge of the step.

http://en.wikipedia.org/wiki/Soluti...nergy_greater_than_step_height_.28E_.3E_V0.29

Perhaps the problem was set up numerically so that E=(4/3)V or something?