[Q]How can i draw real graph from complex function?

[good_phy]

For instance,

I have a simple eigen function such as $\varphi = Ae^{ik_{1}x} + Be^{-ik_{1}x}$

This is complex form which means we can't draw this function on real coordinate.

How can i draw this function? just By taking out real term of complex function?


Second question is what does transmission coefficient means. What exactly i want to know

is how to know amplitude of transmission wave from transmission coefficient in potential

barrier problem? For instance, in problem such that x < a, v = 0 and x >= a, v = c,

Transmission coefficient $T = |\frac{C}{A}|^2\frac{k_2}{k_1}$

But This expression contains absolute value of ratio A to C, So I'm not sure that This

expression indicate real transmission amplitute C when we know Incident amplitute A.

More over, I'm confusion that whether amplitute of wave can be complex number.

 

[malawi_glenn]

You know that you can write that function in terms of cos and sine right? i.e that wavefunction is a sinosodial one with one term propagating to the right and one propagating to the left.

You must match the inner solution with the outer solution so that the wavefuntion is continuous and has continuous derivative at the boundary. Very standard exercise in intro QM.

 

[Domnu]

In addition, you could plot 3D graph as follows: let the x coordinate be the real part of the input, let the y coordinate be the complex part of the input, and let z be the magnitude of the output. You can change this around to get the complex part of the output, etc.