<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:#000000;font-family:Calibri,Helvetica,sans-serif;" 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">
<font size="2">Dear Wien users,</font></div>
<div 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">
<font size="2">I have a question about the name of <br>
</font></div>
<div 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">
<font size="2">"<span>Augmented Plane Wave</span>"</font></div>
<div 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">
<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: Calibri, Helvetica, sans-serif, "EmojiFont", "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols;" dir="ltr">
<font size="2">Trying to see this I found that when a wave crosses a step function,</font></div>
<div 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">
<font size="2"><a href="https://quantummechanics.ucsd.edu/ph130a/130_notes/node149.html" class="OWAAutoLink" id="LPlnk842065" previewremoved="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: Calibri, Helvetica, sans-serif, "EmojiFont", "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols;" dir="ltr">
<font size="2">When the incoming wave <br>
</font></div>
<div 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">
<font size="2">exp(ikx)<br>
</font></div>
<div 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">
<font size="2">reaches an upwards step function there is a reflected wave</font></div>
<div 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">
<font size="2">R exp(-ikx)<br>
</font></div>
<div 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">
<font size="2">and a transmitted wave</font></div>
<div 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">
<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: Calibri, Helvetica, sans-serif, "EmojiFont", "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols;" dir="ltr">
<font size="2">what this article shows is;</font></div>
<div 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">
<font size="2">1 + R = T<br>
</font></div>
<div 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">
<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>
<div 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">
<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: Calibri, Helvetica, sans-serif, "EmojiFont", "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols;" dir="ltr">
<font size="2"><font size="2"><br>
</font></font></div>
<div 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">
<font size="2"><font size="2">Saludos</font></font></div>
<div 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">
<font size="2"><font size="2"><br>
</font></font></div>
<div 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">
<font size="2"><font size="2">Pablo<br>
</font></font></div>
<br>
</div>
</body>
</html>