[Wien] Augmented Plane Wave

[Fecher, Gerhard]

https://en.wiktionary.org/wiki/augmented
==>  increased in number, amount or strength.


Ciao
Gerhard

DEEP THOUGHT in D. Adams; Hitchhikers Guide to the Galaxy:
"I think the problem, to be quite honest with you,
is that you have never actually known what the question is."

====================================
Dr. Gerhard H. Fecher
Institut of Inorganic and Analytical Chemistry
Johannes Gutenberg - University
55099 Mainz
and
Max Planck Institute for Chemical Physics of Solids
01187 Dresden
________________________________________
Von: Wien [wien-bounces at zeus.theochem.tuwien.ac.at] im Auftrag von delamora [delamora at unam.mx]
Gesendet: Freitag, 22. März 2019 02:49
An: wien at zeus.theochem.tuwien.ac.at
Betreff: [Wien] Augmented Plane Wave

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