[Wien] Augmented Plane Wave

[Stefaan Cottenier]

That’s an interesting question. Out of Gerhard’s list (‘increased in number, amount or strength’), I’d go for ‘strength’. In the sense of ‘being more able to do the job’.

Because an APW basis function is more similar to the actual function it needs to describe, in any part of the crystal (inside the muffin tin spheres or outside), they are more efficient as a basis. You need less of them compared to a plane wave basis. That’s being more able to do the job, that’s being ‘augmented’ (compared to regular plane waves).

You define the APW yourself. This is not related to a wave being reflected or transmitted at a boundary.

Stefaan

From: Wien <wien-bounces at zeus.theochem.tuwien.ac.at> On Behalf Of delamora
Sent: Friday, March 22, 2019 2:49 AM
To: wien at zeus.theochem.tuwien.ac.at
Subject: [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

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