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<p>Dear Pablo,</p>
<p>My understanding is that you have a mixed basis set, with plane
wave outside the atomic spheres which are augmented by atomic
functions inside the sphere. You have a good explanation in the
David Singh book but also in the WIEN2k userguide I believe. <br>
</p>
<p>Best Regards,</p>
<p>Xavier</p>
<p><br>
</p>
<div class="moz-cite-prefix">Le 22/03/2019 à 02:49, delamora a
écrit :<br>
</div>
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<font size="2">Dear Wien users,</font></div>
<div style="font-size: 12pt; color: rgb(0, 0, 0); font-family:
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<font size="2">I have a question about the name of <br>
</font></div>
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<font size="2">"<span>Augmented Plane Wave</span>"</font></div>
<div style="font-size: 12pt; color: rgb(0, 0, 0); font-family:
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<font size="2">I had the idea that when the wave enters the
Muffin Tin sphere the amplitude of the wave increased.</font></div>
<div style="font-size: 12pt; color: rgb(0, 0, 0); font-family:
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<font size="2">Trying to see this I found that when a wave
crosses a step function,</font></div>
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<font size="2"><a
href="https://quantummechanics.ucsd.edu/ph130a/130_notes/node149.html"
class="OWAAutoLink" id="LPlnk842065" previewremoved="true"
moz-do-not-send="true">https://quantummechanics.ucsd.edu/ph130a/130_notes/node149.html</a><br>
</font></div>
<div style="font-size: 12pt; color: rgb(0, 0, 0); font-family:
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<font size="2">When the incoming wave <br>
</font></div>
<div style="font-size: 12pt; color: rgb(0, 0, 0); font-family:
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<font size="2">exp(ikx)<br>
</font></div>
<div style="font-size: 12pt; color: rgb(0, 0, 0); font-family:
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<font size="2">reaches an upwards step function there is a
reflected wave</font></div>
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<font size="2">R exp(-ikx)<br>
</font></div>
<div style="font-size: 12pt; color: rgb(0, 0, 0); font-family:
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<font size="2">and a transmitted wave</font></div>
<div style="font-size: 12pt; color: rgb(0, 0, 0); font-family:
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<font size="2">T <font size="2">exp(ik'x)</font><br>
</font></div>
<div style="font-size: 12pt; color: rgb(0, 0, 0); font-family:
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<font size="2">what this article shows is;</font></div>
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<font size="2">1 + R = T<br>
</font></div>
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<font size="2">That is, the amplitudes of the incoming wave
and the reflected wave add to the amplitude of the
transmitted wave<br>
</font></div>
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<font size="2">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 <font
size="2">"<span>Augmented Plane Wave</span>"?</font></font></div>
<div style="font-size: 12pt; color: rgb(0, 0, 0); font-family:
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<font size="2"><font size="2"><br>
</font></font></div>
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<font size="2"><font size="2">Saludos</font></font></div>
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<font size="2"><font size="2"><br>
</font></font></div>
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<font size="2"><font size="2">Pablo<br>
</font></font></div>
<br>
</div>
<br>
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