What Is the E/U Ratio for a Half Reflection Coefficient in Quantum Tunneling?

[PsychonautQQ]

Homework Statement

A particle of energy E approaches a step barrier of height U. What should be the ratio E/U be so that the reflection coefficient is 1/2.

Homework Equations

Transmission + Reflection = 1
Transmission = e^(-2a*alpha)
a = mw∏/h
alpha^2 = (8m∏^2/h^2)(U-E)

Reflection = (k1-k2)^2 / (k1+k2)^2

The Attempt at a Solution

So this is a little bit messy.. I assume most people that are going to help me are familiar with these basic transmission and reflection equations. Anyway is there a possible way to solve this problem an get a ratio that is JUST a number? wouldn't you always have other variables in it since it's talking about a completely undefined particle? there are no ways to get the m's and w's out of the equations right?

 

[Simon Bridge]

All those k's depend on energy.
Expand them out in the reflection coefficient and see what happens.