<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
<style type="text/css" style="display:none;"><!-- P {margin-top:0;margin-bottom:0;} --></style>
</head>
<body dir="ltr">
<div id="divtagdefaultwrapper" style="font-size: 12pt; color: rgb(0, 0, 0); font-family: Calibri, Helvetica, sans-serif, "EmojiFont", "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols;" dir="ltr">
<p style="margin-top:0;margin-bottom:0">Dear Sam,</p>
<p style="margin-top:0;margin-bottom:0">Thank you for your contribution; once I saw a figure in which the plane wave continues into the MT region but enlarged, which confused me.<br>
</p>
<br>
<br>
<div style="color: rgb(0, 0, 0);">
<hr style="display:inline-block;width:98%" tabindex="-1">
<div id="divRplyFwdMsg" dir="ltr"><font style="font-size:11pt" color="#000000" face="Calibri, sans-serif"><b>De:</b> Wien <wien-bounces@zeus.theochem.tuwien.ac.at> en nombre de Sam Trickey <trickey@qtp.ufl.edu><br>
<b>Enviado:</b> viernes, 22 de marzo de 2019 08:13 a. m.<br>
<b>Para:</b> wien@zeus.theochem.tuwien.ac.at<br>
<b>Asunto:</b> Re: [Wien] Augmented Plane Wave</font>
<div> </div>
</div>
<div style="background-color:#FFFFFF"><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="x_moz-cite-prefix">On 3/22/19 7:04 AM, pieper wrote:<br>
</div>
<blockquote type="cite">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="x_moz-txt-link-freetext OWAAutoLink" 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=" id="LPlnk391032" previewremoved="true">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>
_______________________________________________ <br>
Wien mailing list <br>
<a class="x_moz-txt-link-abbreviated OWAAutoLink" href="mailto:Wien@zeus.theochem.tuwien.ac.at" id="LPlnk926864" previewremoved="true">Wien@zeus.theochem.tuwien.ac.at</a>
<br>
<a class="x_moz-txt-link-freetext OWAAutoLink" href="https://urldefense.proofpoint.com/v2/url?u=http-3A__zeus.theochem.tuwien.ac.at_mailman_listinfo_wien&d=DwIGaQ&c=sJ6xIWYx-zLMB3EPkvcnVg&r=3u4OCHnAtdypMfYN_K57COVk2XByDoKwnLuc_zRENzE&m=x11-msafgQ72gWZKP5gGcbCizsHiCDlxxznut2Zo-ug&s=QELHbpUlFIYdizaiEh0uSI_fcbgFXMcKs25dMRPSkU0&e=" id="LPlnk628984" previewremoved="true">https://urldefense.proofpoint.com/v2/url?u=http-3A__zeus.theochem.tuwien.ac.at_mailman_listinfo_wien&d=DwIGaQ&c=sJ6xIWYx-zLMB3EPkvcnVg&r=3u4OCHnAtdypMfYN_K57COVk2XByDoKwnLuc_zRENzE&m=x11-msafgQ72gWZKP5gGcbCizsHiCDlxxznut2Zo-ug&s=QELHbpUlFIYdizaiEh0uSI_fcbgFXMcKs25dMRPSkU0&e=</a>
<br>
SEARCH the MAILING-LIST at: <br>
<a class="x_moz-txt-link-freetext OWAAutoLink" href="https://urldefense.proofpoint.com/v2/url?u=http-3A__www.mail-2Darchive.com_wien-40zeus.theochem.tuwien.ac.at_index.html&d=DwIGaQ&c=sJ6xIWYx-zLMB3EPkvcnVg&r=3u4OCHnAtdypMfYN_K57COVk2XByDoKwnLuc_zRENzE&m=x11-msafgQ72gWZKP5gGcbCizsHiCDlxxznut2Zo-ug&s=p2zeCI2PUnzFXnYuR6JhoHGW3GZi1dVfbW6410meyh4&e=" id="LPlnk679104" previewremoved="true">https://urldefense.proofpoint.com/v2/url?u=http-3A__www.mail-2Darchive.com_wien-40zeus.theochem.tuwien.ac.at_index.html&d=DwIGaQ&c=sJ6xIWYx-zLMB3EPkvcnVg&r=3u4OCHnAtdypMfYN_K57COVk2XByDoKwnLuc_zRENzE&m=x11-msafgQ72gWZKP5gGcbCizsHiCDlxxznut2Zo-ug&s=p2zeCI2PUnzFXnYuR6JhoHGW3GZi1dVfbW6410meyh4&e=</a>
<br>
</blockquote>
_______________________________________________ <br>
Wien mailing list <br>
<a class="x_moz-txt-link-abbreviated OWAAutoLink" href="mailto:Wien@zeus.theochem.tuwien.ac.at" id="LPlnk31658" previewremoved="true">Wien@zeus.theochem.tuwien.ac.at</a>
<br>
<a class="x_moz-txt-link-freetext OWAAutoLink" href="https://urldefense.proofpoint.com/v2/url?u=http-3A__zeus.theochem.tuwien.ac.at_mailman_listinfo_wien&d=DwIGaQ&c=sJ6xIWYx-zLMB3EPkvcnVg&r=3u4OCHnAtdypMfYN_K57COVk2XByDoKwnLuc_zRENzE&m=x11-msafgQ72gWZKP5gGcbCizsHiCDlxxznut2Zo-ug&s=QELHbpUlFIYdizaiEh0uSI_fcbgFXMcKs25dMRPSkU0&e=" id="LPlnk61016" previewremoved="true">https://urldefense.proofpoint.com/v2/url?u=http-3A__zeus.theochem.tuwien.ac.at_mailman_listinfo_wien&d=DwIGaQ&c=sJ6xIWYx-zLMB3EPkvcnVg&r=3u4OCHnAtdypMfYN_K57COVk2XByDoKwnLuc_zRENzE&m=x11-msafgQ72gWZKP5gGcbCizsHiCDlxxznut2Zo-ug&s=QELHbpUlFIYdizaiEh0uSI_fcbgFXMcKs25dMRPSkU0&e=</a>
<br>
SEARCH the MAILING-LIST at: <a class="x_moz-txt-link-freetext OWAAutoLink" href="https://urldefense.proofpoint.com/v2/url?u=http-3A__www.mail-2Darchive.com_wien-40zeus.theochem.tuwien.ac.at_index.html&d=DwIGaQ&c=sJ6xIWYx-zLMB3EPkvcnVg&r=3u4OCHnAtdypMfYN_K57COVk2XByDoKwnLuc_zRENzE&m=x11-msafgQ72gWZKP5gGcbCizsHiCDlxxznut2Zo-ug&s=p2zeCI2PUnzFXnYuR6JhoHGW3GZi1dVfbW6410meyh4&e=" id="LPlnk598973" previewremoved="true">
https://urldefense.proofpoint.com/v2/url?u=http-3A__www.mail-2Darchive.com_wien-40zeus.theochem.tuwien.ac.at_index.html&d=DwIGaQ&c=sJ6xIWYx-zLMB3EPkvcnVg&r=3u4OCHnAtdypMfYN_K57COVk2XByDoKwnLuc_zRENzE&m=x11-msafgQ72gWZKP5gGcbCizsHiCDlxxznut2Zo-ug&s=p2zeCI2PUnzFXnYuR6JhoHGW3GZi1dVfbW6410meyh4&e=</a><br>
</blockquote>
<br>
<pre class="x_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)
Fax: 352-392-8722
<a class="x_moz-txt-link-freetext OWAAutoLink" href="http://www.qtp.ufl.edu/ofdft" id="LPlnk203176" previewremoved="true">http://www.qtp.ufl.edu/ofdft</a>
<a class="x_moz-txt-link-freetext OWAAutoLink" href="http://users.clas.ufl.edu/trickey" id="LPlnk515609" previewremoved="true">http://users.clas.ufl.edu/trickey</a>
</pre>
</div>
</div>
</div>
</body>
</html>