Transmission coefficients for a spin up particle at any incidence angle?

I have a working notebook calculating the Transmission coefficients for a spin up particle coming in at normal incidence and meeting an infinite potential barrier with spin orbit interaction under it.

I need to generalise this for a spin up particle at any incidence angle. I have made an attempt at this. But the graphs are coming out wrong so I must have made some mistake. I’m not experienced enough to know where the mistakes are or how mathematica is interpreting what I have told it.

I’ve attached both notebooks so you can compare working with not working.

Basically what I need is a vector k = Abs[kx + i ky] and an angle tk = Arg[kx + i ky] so that I can keep the angle, tk, constant and plot graphs over k which kx and ky are dependent on.

I’ve succeeded in making it worse. So that’s something.

I’ve found a mistake in my maths. It’s made it worse. I’m stumped!