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mhjensen committed Jan 10, 2024
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63 changes: 32 additions & 31 deletions doc/Projects/2023/Project1/html/Project1-bs.html
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<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<meta name="description" content="Project 1, deadline March 31, 2023">
<title>Project 1, deadline March 31, 2023</title>
<meta name="description" content="Project 1, deadline March 22, 2024">
<title>Project 1, deadline March 22, 2024</title>
<!-- Bootstrap style: bootstrap -->
<!-- doconce format html Project1.do.txt --html_style=bootstrap --pygments_html_style=default --html_admon=bootstrap_panel --html_output=Project1-bs -->
<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
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<span class="icon-bar"></span>
<span class="icon-bar"></span>
</button>
<a class="navbar-brand" href="Project1-bs.html">Project 1, deadline March 31, 2023</a>
<a class="navbar-brand" href="Project1-bs.html">Project 1, deadline March 22, 2024</a>
</div>
<div class="navbar-collapse collapse navbar-responsive-collapse">
<ul class="nav navbar-nav navbar-right">
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<!-- ------------------- main content ---------------------- -->
<div class="jumbotron">
<center>
<h1>Project 1, deadline March 31, 2023</h1>
<h1>Project 1, deadline March 22, 2024</h1>
</center> <!-- document title -->

<!-- author(s): <a href="http://www.uio.no/studier/emner/matnat/fys/FYS4411/index-eng.html" target="_self">Computational Physics II FYS4411/FYS9411</a> -->
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</center>
<br>
<center>
<h4>Jan 26, 2023</h4>
<h4>Jan 10, 2024</h4>
</center> <!-- date -->
<br>


</div> <!-- end jumbotron -->
<h2 id="introduction" class="anchor">Introduction </h2>

<p> The spectacular demonstration of Bose-Einstein condensation (BEC) in gases of
alkali atoms $^{87}$Rb, $^{23}$Na, $^7$Li confined in magnetic
traps has led to an explosion of interest in
confined Bose systems. Of interest is the fraction of condensed atoms, the
nature of the condensate, the excitations above the condensate, the atomic
density in the trap as a function of Temperature and the critical temperature of BEC,
\( T_c \).
</p>

<p> A key feature of the trapped alkali and atomic hydrogen systems is that they are
dilute. The characteristic dimensions of a typical trap for $^{87}$Rb is
\( a_{ho}=\left( {\hbar}/{m\omega_\perp}\right)^\frac{1}{2}=1-2 \times 10^4 \)
\AA\ . The interaction between $^{87}$Rb atoms can be well represented
by its s-wave scattering length, \( a_{Rb} \). This scattering length lies in the
range \( 85 a_0 < a_{Rb} < 140 a_0 \) where \( a_0 = 0.5292 \) \AA\ is the Bohr radius.
The definite value \( a_{Rb} = 100 a_0 \) is usually selected and
for calculations the definite ratio of atom size to trap size
\( a_{Rb}/a_{ho} = 4.33 \times 10^{-3} \)
is usually chosen. A typical $^{87}$Rb atom
density in the trap is \( n \simeq 10^{12}- 10^{14} \) atoms per cubic cm, giving an
inter-atom spacing \( \ell \simeq 10^4 \) \AA. Thus the effective atom size is small
compared to both the trap size and the inter-atom spacing, the condition
for diluteness (\( na^3_{Rb} \simeq 10^{-6} \) where \( n = N/V \) is the number
density).
<p>The spectacular demonstration of Bose-Einstein condensation (BEC) in
gases of alkali atoms $^{87}$Rb, $^{23}$Na, $^7$Li confined in
magnetic traps has led to an explosion of interest in confined Bose
systems. Of interest is the fraction of condensed atoms, the nature of
the condensate, the excitations above the condensate, the atomic
density in the trap as a function of Temperature and the critical
temperature of BEC, \( T_c \).
</p>

<p>A key feature of the trapped alkali and atomic hydrogen systems is
that they are dilute. The characteristic dimensions of a typical trap
for $^{87}$Rb is \( a_{ho}=\left(
{\hbar}/{m\omega_\perp}\right)^\frac{1}{2}=1-2 \times 10^4 \) \AA\
. The interaction between $^{87}$Rb atoms can be well represented by
its s-wave scattering length, \( a_{Rb} \). This scattering length lies
in the range \( 85 a_0 < a_{Rb} < 140 a_0 \) where \( a_0 = 0.5292 \) \AA\ is
the Bohr radius. The definite value \( a_{Rb} = 100 a_0 \) is usually
selected and for calculations the definite ratio of atom size to trap
size \( a_{Rb}/a_{ho} = 4.33 \times 10^{-3} \) is usually chosen. A
typical $^{87}$Rb atom density in the trap is \( n \simeq 10^{12}-
10^{14} \) atoms per cubic cm, giving an inter-atom spacing \( \ell
\simeq 10^4 \) \AA. Thus the effective atom size is small compared to
both the trap size and the inter-atom spacing, the condition for
diluteness (\( na^3_{Rb} \simeq 10^{-6} \) where \( n = N/V \) is the number
density).
</p>

<p>Many theoretical studies of Bose-Einstein condensates (BEC) in gases
Expand Down Expand Up @@ -210,7 +211,7 @@ <h2 id="introduction" class="anchor">Introduction </h2>
trial wave function.
</p>

<p> This trial wave function is used to study the sensitivity of
<p>This trial wave function is used to study the sensitivity of
condensate and non-condensate properties to the hard sphere radius
and the number of particles. The trap we will use is a spherical (S)
or an elliptical (E) harmonic trap in one, two and finally three
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</footer>
-->
<center style="font-size:80%">
<!-- copyright --> &copy; 1999-2023, "Computational Physics II FYS4411/FYS9411":"http://www.uio.no/studier/emner/matnat/fys/FYS4411/index-eng.html". Released under CC Attribution-NonCommercial 4.0 license
<!-- copyright --> &copy; 1999-2024, "Computational Physics II FYS4411/FYS9411":"http://www.uio.no/studier/emner/matnat/fys/FYS4411/index-eng.html". Released under CC Attribution-NonCommercial 4.0 license
</center>
</body>
</html>
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61 changes: 31 additions & 30 deletions doc/Projects/2023/Project1/html/Project1.html
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Original file line number Diff line number Diff line change
Expand Up @@ -8,8 +8,8 @@
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<meta name="description" content="Project 1, deadline March 31, 2023">
<title>Project 1, deadline March 31, 2023</title>
<meta name="description" content="Project 1, deadline March 22, 2024">
<title>Project 1, deadline March 22, 2024</title>
<style type="text/css">
/* bloodish style */
body {
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<!-- ------------------- main content ---------------------- -->
<center>
<h1>Project 1, deadline March 31, 2023</h1>
<h1>Project 1, deadline March 22, 2024</h1>
</center> <!-- document title -->

<!-- author(s): <a href="http://www.uio.no/studier/emner/matnat/fys/FYS4411/index-eng.html" target="_blank">Computational Physics II FYS4411/FYS9411</a> -->
Expand All @@ -190,35 +190,36 @@ <h1>Project 1, deadline March 31, 2023</h1>
</center>
<br>
<center>
<h4>Jan 26, 2023</h4>
<h4>Jan 10, 2024</h4>
</center> <!-- date -->
<br>
<h2 id="introduction">Introduction </h2>

<p> The spectacular demonstration of Bose-Einstein condensation (BEC) in gases of
alkali atoms $^{87}$Rb, $^{23}$Na, $^7$Li confined in magnetic
traps has led to an explosion of interest in
confined Bose systems. Of interest is the fraction of condensed atoms, the
nature of the condensate, the excitations above the condensate, the atomic
density in the trap as a function of Temperature and the critical temperature of BEC,
\( T_c \).
</p>

<p> A key feature of the trapped alkali and atomic hydrogen systems is that they are
dilute. The characteristic dimensions of a typical trap for $^{87}$Rb is
\( a_{ho}=\left( {\hbar}/{m\omega_\perp}\right)^\frac{1}{2}=1-2 \times 10^4 \)
\AA\ . The interaction between $^{87}$Rb atoms can be well represented
by its s-wave scattering length, \( a_{Rb} \). This scattering length lies in the
range \( 85 a_0 < a_{Rb} < 140 a_0 \) where \( a_0 = 0.5292 \) \AA\ is the Bohr radius.
The definite value \( a_{Rb} = 100 a_0 \) is usually selected and
for calculations the definite ratio of atom size to trap size
\( a_{Rb}/a_{ho} = 4.33 \times 10^{-3} \)
is usually chosen. A typical $^{87}$Rb atom
density in the trap is \( n \simeq 10^{12}- 10^{14} \) atoms per cubic cm, giving an
inter-atom spacing \( \ell \simeq 10^4 \) \AA. Thus the effective atom size is small
compared to both the trap size and the inter-atom spacing, the condition
for diluteness (\( na^3_{Rb} \simeq 10^{-6} \) where \( n = N/V \) is the number
density).
<p>The spectacular demonstration of Bose-Einstein condensation (BEC) in
gases of alkali atoms $^{87}$Rb, $^{23}$Na, $^7$Li confined in
magnetic traps has led to an explosion of interest in confined Bose
systems. Of interest is the fraction of condensed atoms, the nature of
the condensate, the excitations above the condensate, the atomic
density in the trap as a function of Temperature and the critical
temperature of BEC, \( T_c \).
</p>

<p>A key feature of the trapped alkali and atomic hydrogen systems is
that they are dilute. The characteristic dimensions of a typical trap
for $^{87}$Rb is \( a_{ho}=\left(
{\hbar}/{m\omega_\perp}\right)^\frac{1}{2}=1-2 \times 10^4 \) \AA\
. The interaction between $^{87}$Rb atoms can be well represented by
its s-wave scattering length, \( a_{Rb} \). This scattering length lies
in the range \( 85 a_0 < a_{Rb} < 140 a_0 \) where \( a_0 = 0.5292 \) \AA\ is
the Bohr radius. The definite value \( a_{Rb} = 100 a_0 \) is usually
selected and for calculations the definite ratio of atom size to trap
size \( a_{Rb}/a_{ho} = 4.33 \times 10^{-3} \) is usually chosen. A
typical $^{87}$Rb atom density in the trap is \( n \simeq 10^{12}-
10^{14} \) atoms per cubic cm, giving an inter-atom spacing \( \ell
\simeq 10^4 \) \AA. Thus the effective atom size is small compared to
both the trap size and the inter-atom spacing, the condition for
diluteness (\( na^3_{Rb} \simeq 10^{-6} \) where \( n = N/V \) is the number
density).
</p>

<p>Many theoretical studies of Bose-Einstein condensates (BEC) in gases
Expand Down Expand Up @@ -248,7 +249,7 @@ <h2 id="introduction">Introduction </h2>
trial wave function.
</p>

<p> This trial wave function is used to study the sensitivity of
<p>This trial wave function is used to study the sensitivity of
condensate and non-condensate properties to the hard sphere radius
and the number of particles. The trap we will use is a spherical (S)
or an elliptical (E) harmonic trap in one, two and finally three
Expand Down Expand Up @@ -631,7 +632,7 @@ <h2 id="format-for-electronic-delivery-of-report-and-programs">Format for electr

<!-- ------------------- end of main content --------------- -->
<center style="font-size:80%">
<!-- copyright --> &copy; 1999-2023, "Computational Physics II FYS4411/FYS9411":"http://www.uio.no/studier/emner/matnat/fys/FYS4411/index-eng.html". Released under CC Attribution-NonCommercial 4.0 license
<!-- copyright --> &copy; 1999-2024, "Computational Physics II FYS4411/FYS9411":"http://www.uio.no/studier/emner/matnat/fys/FYS4411/index-eng.html". Released under CC Attribution-NonCommercial 4.0 license
</center>
</body>
</html>
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