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Update 2022-02-14 20:42

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Jean-Sébastien
2022-02-14 20:42:37 +01:00
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commit 09a8ba5fb6
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build/ems_ca_fe_uP.html
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@@ -1,7 +1,7 @@
<!DOCTYPE html>
<html lang="en">
<head>
<!-- 2022-02-13 Sun 21:20 -->
<!-- 2022-02-14 Mon 20:35 -->
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Pre-Quantum Electrodynamics</title>
@@ -1610,14 +1610,14 @@ problem for the electrostatic potential. Namely, put \(\phi = \psi = \Phi\). T
The first term on the left-hand side vanishes since \(\Phi\) satisfies Laplace.
The right-hand side can be made to vanish if \(\Phi\) obeys either
</p>
<div class="eqlabel" id="org25f3c75">
<div class="eqlabel" id="org8a3aa85">
<p>
<a id="Dirichlet"></a><a href="./ems_ca_fe_uP.html#Dirichlet"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a>
</p>
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@@ -1629,14 +1629,14 @@ The right-hand side can be made to vanish if \(\Phi\) obeys either
<p>
or
</p>
<div class="eqlabel" id="orgff19131">
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<p>
<a id="Neumann"></a><a href="./ems_ca_fe_uP.html#Neumann"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a>
</p>
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@@ -1657,19 +1657,19 @@ is unique. For Neumann, the solution is unique apart from an unimportant consta
<p>
We can thus finally state the
</p>
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<a id="uniq_thm"></a><a href="./ems_ca_fe_uP.html#uniq_thm"><svg xmlns="http://www.w3.org/2000/svg" width="16" height="16" fill="currentColor" class="bi bi-link" viewBox="0 0 16 16">
<path d="M6.354 5.5H4a3 3 0 0 0 0 6h3a3 3 0 0 0 2.83-4H9c-.086 0-.17.01-.25.031A2 2 0 0 1 7 10.5H4a2 2 0 1 1 0-4h1.535c.218-.376.495-.714.82-1z"/>
<path d="M9 5.5a3 3 0 0 0-2.83 4h1.098A2 2 0 0 1 9 6.5h3a2 2 0 1 1 0 4h-1.535a4.02 4.02 0 0 1-.82 1H12a3 3 0 1 0 0-6H9z"/>
</svg></a>
</p>
<div class="alteqlabels" id="orgcd9ef4e">
<div class="alteqlabels" id="orgc0186aa">
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<div class="core div" id="org5889497">
<p>
<b>Uniqueness Theorem</b>
</p>
@@ -1707,7 +1707,7 @@ whereas the earlier example involved only surface charges).
we have used Green's identity to provide a general statement on uniqueness. Reading Griffiths, you might be misled into thinking that there are numerous cases and corollaries.
</p>
<div class="info div" id="orgfb56c0b">
<div class="info div" id="org8d9ede7">
<p>
<b>Comment/warning</b>: <b>uniqueness theorem on uniqueness theorems</b> <br>
Do not be misled: there is a <i>unique</i> uniqueness theorem for the
@@ -1734,7 +1734,7 @@ target="_blank">Creative Commons Attribution 4.0 International License</a>.
</div>
<div id="postamble" class="status">
<p class="author">Author: Jean-Sébastien Caux</p>
<p class="date">Created: 2022-02-13 Sun 21:20</p>
<p class="date">Created: 2022-02-14 Mon 20:35</p>
<p class="validation"></p>
</div>