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<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US">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’.
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US">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).<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US">You define the APW yourself. This is not related to a wave being reflected or transmitted at a boundary.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US">Stefaan<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:EN-US"><o:p> </o:p></span></p>
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<p class="MsoNormal"><b><span lang="NL">From:</span></b><span lang="NL"> Wien <wien-bounces@zeus.theochem.tuwien.ac.at>
<b>On Behalf Of </b>delamora<br>
<b>Sent:</b> Friday, March 22, 2019 2:49 AM<br>
<b>To:</b> wien@zeus.theochem.tuwien.ac.at<br>
<b>Subject:</b> [Wien] Augmented Plane Wave<o:p></o:p></span></p>
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<p class="MsoNormal"><o:p> </o:p></p>
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<p class="MsoNormal"><span style="font-size:10.0pt;color:black">Dear Wien users,</span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:10.0pt;color:black">I have a question about the name of
</span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:10.0pt;color:black">"Augmented Plane Wave"</span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:10.0pt;color:black">I had the idea that when the wave enters the Muffin Tin sphere the amplitude of the wave increased.</span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:10.0pt;color:black">Trying to see this I found that when a wave crosses a step function,</span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:10.0pt;color:black"><a href="https://quantummechanics.ucsd.edu/ph130a/130_notes/node149.html">https://quantummechanics.ucsd.edu/ph130a/130_notes/node149.html</a></span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:10.0pt;color:black">When the incoming wave
</span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:10.0pt;color:black">exp(ikx)</span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:10.0pt;color:black">reaches an upwards step function there is a reflected wave</span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:10.0pt;color:black">R exp(-ikx)</span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:10.0pt;color:black">and a transmitted wave</span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:10.0pt;color:black">T exp(ik'x)</span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:10.0pt;color:black">what this article shows is;</span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:10.0pt;color:black">1 + R = T</span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:10.0pt;color:black">That is, the amplitudes of the incoming wave and the reflected wave add to the amplitude of the transmitted wave</span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:10.0pt;color:black">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"?</span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:10.0pt;color:black">Saludos</span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:10.0pt;color:black">Pablo</span><span style="font-size:12.0pt;color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;color:black"><o:p> </o:p></span></p>
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