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	<title>Comments on: Water Mechanics</title>
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		<title>By: Walt</title>
		<link>http://www.arsmathematica.net/2005/07/06/water-mechanics/#comment-66</link>
		<dc:creator><![CDATA[Walt]]></dc:creator>
		<pubDate>Thu, 07 Jul 2005 04:10:42 +0000</pubDate>
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		<description><![CDATA[For a classical system, I don&#039;t think 33 degrees of freedom would be overwhelming, especially since you could probably make some simplifying assumptions.  So I think you&#039;re right that the reason it&#039;s so complicated is strictly a quantum phenomenon.  It&#039;s still kinda depressing, though.]]></description>
		<content:encoded><![CDATA[<p>For a classical system, I don&#8217;t think 33 degrees of freedom would be overwhelming, especially since you could probably make some simplifying assumptions.  So I think you&#8217;re right that the reason it&#8217;s so complicated is strictly a quantum phenomenon.  It&#8217;s still kinda depressing, though.</p>
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		<title>By: Walt</title>
		<link>http://www.arsmathematica.net/2005/07/06/water-mechanics/#comment-65</link>
		<dc:creator><![CDATA[Walt]]></dc:creator>
		<pubDate>Wed, 06 Jul 2005 19:53:39 +0000</pubDate>
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		<description><![CDATA[But water molecules are so &lt;i&gt;little&lt;/i&gt;.  How complicated can they be? :-)]]></description>
		<content:encoded><![CDATA[<p>But water molecules are so <i>little</i>.  How complicated can they be? <img src="http://www.arsmathematica.net/wp-includes/images/smilies/icon_smile.gif" alt=":-)" class="wp-smiley" /></p>
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		<title>By: sigfpe</title>
		<link>http://www.arsmathematica.net/2005/07/06/water-mechanics/#comment-64</link>
		<dc:creator><![CDATA[sigfpe]]></dc:creator>
		<pubDate>Wed, 06 Jul 2005 18:26:59 +0000</pubDate>
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		<description><![CDATA[&quot;Despite the fact that...&quot;

A water molecule is two hydrogen atoms and one oxygen atom. Let&#039;s treat the nuclei as single particles. So a water molecule has 2+8=10 electrons and 3 nuceli. So we&#039;re looking at a 13 body system. Let&#039;s drop the two electrons from the inner shell of the oxygen atom so we&#039;re down to 11 bodies. This means we&#039;re looking at a system with 33 degrees of freedom with a highly non-trivial Hamiltonian. To investigate water in &#039;bulk&#039; we need at least 2 molecules. So that&#039;s a 66 dimensional system. We need to solve the Schrodinger equation on a 66-dimensional space. If we discretise this space with just 8 points along each axis we still need 2^198 samples to represent the wavefunction.

So I think you mean &quot;Because of the fact that...&quot; rather than &quot;Despite the fact that...&quot; :-)]]></description>
		<content:encoded><![CDATA[<p>&#8220;Despite the fact that&#8230;&#8221;</p>
<p>A water molecule is two hydrogen atoms and one oxygen atom. Let&#8217;s treat the nuclei as single particles. So a water molecule has 2+8=10 electrons and 3 nuceli. So we&#8217;re looking at a 13 body system. Let&#8217;s drop the two electrons from the inner shell of the oxygen atom so we&#8217;re down to 11 bodies. This means we&#8217;re looking at a system with 33 degrees of freedom with a highly non-trivial Hamiltonian. To investigate water in &#8216;bulk&#8217; we need at least 2 molecules. So that&#8217;s a 66 dimensional system. We need to solve the Schrodinger equation on a 66-dimensional space. If we discretise this space with just 8 points along each axis we still need 2^198 samples to represent the wavefunction.</p>
<p>So I think you mean &#8220;Because of the fact that&#8230;&#8221; rather than &#8220;Despite the fact that&#8230;&#8221; <img src="http://www.arsmathematica.net/wp-includes/images/smilies/icon_smile.gif" alt=":-)" class="wp-smiley" /></p>
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