Complex Quantum Mechanical Problem needs Plotting

[neutrino2063]

So I have this equation:

T=$$(cos(k2*a)^2+(1/4)*(r^\ast+\frac{1}{r^\ast})*sin(k2*a)*sin(k2^\ast*a))^{-1}$$

where r=k2/k1; $$r^\ast=\frac{k2^\ast}{k1}; k2^\ast$$ is the complex conjugate of k2

also $$k2=\frac{\sqrt{2*m*(E-V)}}{\hbar}$$ and $$k1=\frac{\sqrt{2*m*E}}{\hbar}$$

m,$$\hbar$$,a are all constants
Somehow I need to write T as a function of $$\alpha=\frac{V}{E}$$ so that I can plot it.
Truth be told I have no idea what to do. I tried playing around with k2 but got nowhere. So any ideas or pointing in the right direction would be much appreciated.
In case anyone is wondering where this is coming from it is the 1-D step potential barrier problem in into Quantum Mechanics.

Thank you

 

[tiny-tim]

Hi neutrino2063!

$$k2=\frac{\sqrt{2*m*(E-V)}}{\hbar}$$ and $$k1=\frac{\sqrt{2*m*E}}{\hbar}$$
…
Somehow I need to write T as a function of $$\alpha=\frac{V}{E}$$ so that I can plot it.
Truth be told I have no idea what to do. I tried playing around with k2 but got nowhere.

But did you try squaring k₂ (and k₁)?