[Wien] Augmented Plane Wave

[delamora]

Dear Wien users,
I have a question about the name of
"Augmented Plane Wave"
I had the idea that when the wave enters the Muffin Tin sphere the amplitude of the wave increased.
Trying to see this I found that when a wave crosses a step function,
https://quantummechanics.ucsd.edu/ph130a/130_notes/node149.html
When the incoming wave
exp(ikx)
reaches an upwards step function there is a reflected wave
R exp(-ikx)
and a transmitted wave
T exp(ik'x)
what this article shows is;
1 + R = T
That is, the amplitudes of the incoming wave and the reflected wave add to the amplitude of the transmitted wave
If I take this into a square well then I would understand that the waves inside the well have the total amplitude equal to the incoming and transmitted wave. That is, when the wave enters the Muffin Tin the amplitude of wave is not AUGMENTED. So why is this method called "Augmented Plane Wave"?

Saludos

Pablo

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