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<font size="-1">Rarely do I contribute to this list, though I
benefit from reading it. <br>
<br>
I must respectfully contradict Martin. Professor Slater clearly
intended<br>
that the augmentation be of the plane wave. The history, at least
as I <br>
know it, is this.<br>
<br>
Professor Slater did not use the word "augment" or "augmented" in
his <br>
1937 paper that usually is cited as the original APW paper [Rev.
51, 846 (1937)].<br>
So far as I am aware, the first time he used the phrase "augmented
plane<br>
wave" is in Phys. Rev. 92, 603 (1953). The phrase appears in the
title but,<br>
more important for discerning his intent is the discussion
beginning<br>
on the bottom right of p. 603 and continuing on 604. He
introduces Herring's<br>
orthogonalized plane waves and summarizes their applications and
then says<br>
(lines 7-9, LH column, p. 604) "Relatively few such
orthogonalized or<br>
augmented plane waves suffice to give a rather good approximate
wave<br>
function." Noting the problem of non-existent orthogonalization
of a 2p-like<br>
state to a deeper core state found by Frank Herman, Prof. Slater
goes on to<br>
say "Herman has suggested that in such a case we could augment the
plane<br>
wave ...". He opens the next paragraph with "The present method
may be regarded<br>
as a straight-forward procedure for augmenting a plane wave by
adding to it <br>
a contribution near each nucleus ...". <br>
<br>
It may be useful to add that I was part of Prof. Slater's group
within QTP for the<br>
last 7-1/2 years of his life and one year was assigned (even
though I was an <br>
Asst. Prof. not a post-doc!) to be his teaching assistant in his
"Quantum Theory<br>
of Matter" course. Those experiences were consistent with the
sentences just quoted.<br>
<br>
Peace, Sam <br>
<br>
<br>
</font><br>
<div class="moz-cite-prefix">On 3/22/19 7:04 AM, pieper wrote:<br>
</div>
<blockquote type="cite"
cite="mid:5911857402c91ae2e6140e17d189ed42@ifp.tuwien.ac.at">Dear
Pablo,
<br>
<br>
I suspect your problem occurs because you left out the word which
"Augmented" refers too: It is an "Augmented Plane Wave Method",
<br>
that is, the Method is augmented (including additional basis
functions), not the plane waves (in amplitude or intensity).
<br>
<br>
Best regards,
<br>
<br>
Martin Pieper
<br>
<br>
---
<br>
Dr. Martin Pieper
<br>
Karl-Franzens University
<br>
Institute of Physics
<br>
Universitätsplatz 5
<br>
A-8010 Graz
<br>
Austria
<br>
Tel.: +43-(0)316-380-8564
<br>
<br>
<br>
Am 2019-03-22 02:49, schrieb delamora:
<br>
<blockquote type="cite">Dear Wien users,
<br>
I have a question about the name of
<br>
<br>
"Augmented Plane Wave"
<br>
I had the idea that when the wave enters the Muffin Tin sphere
the
<br>
amplitude of the wave increased.
<br>
Trying to see this I found that when a wave crosses a step
function,
<br>
<a class="moz-txt-link-freetext" href="https://urldefense.proofpoint.com/v2/url?u=https-3A__quantummechanics.ucsd.edu_ph130a_130-5Fnotes_node149.html&d=DwIGaQ&c=sJ6xIWYx-zLMB3EPkvcnVg&r=3u4OCHnAtdypMfYN_K57COVk2XByDoKwnLuc_zRENzE&m=x11-msafgQ72gWZKP5gGcbCizsHiCDlxxznut2Zo-ug&s=CV5sXDCtZrDlO2GFM8sW4hec5wD0wT0O34PcltW3ZfI&e=">https://urldefense.proofpoint.com/v2/url?u=https-3A__quantummechanics.ucsd.edu_ph130a_130-5Fnotes_node149.html&d=DwIGaQ&c=sJ6xIWYx-zLMB3EPkvcnVg&r=3u4OCHnAtdypMfYN_K57COVk2XByDoKwnLuc_zRENzE&m=x11-msafgQ72gWZKP5gGcbCizsHiCDlxxznut2Zo-ug&s=CV5sXDCtZrDlO2GFM8sW4hec5wD0wT0O34PcltW3ZfI&e=</a>
<br>
<br>
When the incoming wave
<br>
<br>
exp(ikx)
<br>
<br>
reaches an upwards step function there is a reflected wave
<br>
R exp(-ikx)
<br>
<br>
and a transmitted wave
<br>
T exp(ik'x)
<br>
<br>
what this article shows is;
<br>
1 + R = T
<br>
<br>
That is, the amplitudes of the incoming wave and the reflected
wave
<br>
add to the amplitude of the transmitted wave
<br>
<br>
If I take this into a square well then I would understand that
the
<br>
waves inside the well have the total amplitude equal to the
incoming
<br>
and transmitted wave. That is, when the wave enters the Muffin
Tin the
<br>
amplitude of wave is not AUGMENTED. So why is this method called
<br>
"Augmented Plane Wave"?
<br>
<br>
Saludos
<br>
<br>
Pablo
<br>
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<pre class="moz-signature" cols="72">--
Samuel B. Trickey
QTP, Depts. of Physics and Chemistry
2324 Physics Building
Box 118435
Univ. of Florida
Gainesville, FL 32611-8435
Vox: 352-392-6978 (direct)
Vox: 352-392-1597 (receptionist)
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