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7 cs191.html
... ... @@ -1,4 +1,4 @@
1   -<div class='wrapper'>
  1 +<div><div class='wrapper'>
2 2 <p><a name='1'></a></p>
3 3 <h1>CS 191: Qubits, Quantum Mechanics and Computers</h1>
4 4 <h2>Introduction -- January 17, 2012</h2>
@@ -2560,11 +2560,10 @@
2560 2560 div.style.width = '15%';
2561 2561 for (var i = 0; i < ll; i++) {
2562 2562 div.innerHTML += '<a href="\#' + a[i].name + '">'
2563   - + a[i].parentElement.nextElementSibling
2564   - .nextElementSibling.innerText
  2563 + + a[i].parentElement.nextElementSibling.innerHTML
2565 2564 + '</a><br />';
2566 2565 }
2567 2566 var div = document.getElementsByClassName('wrapper')[0];
2568 2567 div.style.width = '80%';
2569 2568 }
2570   -</script>
  2569 +</script></div>
7 ee105.html
... ... @@ -1,4 +1,4 @@
1   -<div class='wrapper'>
  1 +<div><div class='wrapper'>
2 2 <p><a name='1'></a></p>
3 3 <h1>EE 105: Devices &amp; Circuits</h1>
4 4 <h2>Wednesday, January 18, 2012.</h2>
@@ -1814,11 +1814,10 @@
1814 1814 div.style.width = '15%';
1815 1815 for (var i = 0; i < ll; i++) {
1816 1816 div.innerHTML += '<a href="\#' + a[i].name + '">'
1817   - + a[i].parentElement.nextElementSibling
1818   - .nextElementSibling.innerText
  1817 + + a[i].parentElement.nextElementSibling.innerHTML
1819 1818 + '</a><br />';
1820 1819 }
1821 1820 var div = document.getElementsByClassName('wrapper')[0];
1822 1821 div.style.width = '80%';
1823 1822 }
1824   -</script>
  1823 +</script></div>
5 ee120.html
... ... @@ -1,4 +1,4 @@
1   -<div class='wrapper'>
  1 +<div><div class='wrapper'>
2 2 <p><a name='1'></a></p>
3 3 <h1>EE 120: Signals and Systems</h1>
4 4 <h2>January 17, 2012.</h2>
@@ -1810,5 +1810,4 @@
1810 1810 var div = document.getElementsByClassName('wrapper')[0];
1811 1811 div.style.width = '80%';
1812 1812 }
1813   -</script>
1814   -</div>
  1813 +</script></div>
7 markdown
@@ -2,7 +2,7 @@
2 2
3 3 if `test -n "$1" && test -f $1`; then
4 4 fname=`echo $1 | sed -r "s/\.[^.]*$//"`.html
5   - echo "<div class='wrapper'>"
  5 + echo "<div><div class='wrapper'>"
6 6 cat $1 | markdown_py -x mathjax
7 7 echo "</div><div class='pos'></div>"
8 8 echo "<script src='mathjax/unpacked/MathJax.js?config=default'></script>
@@ -31,12 +31,11 @@ if (ll > 0) {
31 31 div.style.width = '15%';
32 32 for (var i = 0; i < ll; i++) {
33 33 div.innerHTML += '<a href=\"\#' + a[i].name + '\">'
34   - + a[i].parentElement.nextElementSibling
35   - .nextElementSibling.innerText
  34 + + a[i].parentElement.nextElementSibling.innerHTML
36 35 + '</a><br />';
37 36 }
38 37 var div = document.getElementsByClassName('wrapper')[0];
39 38 div.style.width = '80%';
40 39 }
41   -</script>"
  40 +</script></div>"
42 41 fi
24 phys112.html
... ... @@ -1,4 +1,4 @@
1   -<div class='wrapper'>
  1 +<div><div class='wrapper'>
2 2 <p><a name='1'></a></p>
3 3 <h1>Physics 112: Statistical Mechanics</h1>
4 4 <h2>January 18, 2012</h2>
@@ -2560,7 +2560,24 @@
2560 2560 for all practical purposes, does not exist.</p>
2561 2561 <p>Indeed, in this case, the chemical potentials add.</p>
2562 2562 <p>Problem: running out of time. Try to tell a little bit about how we discuss
2563   -the </p><div class='pos'></div>
  2563 +the formation of atoms in the early universe. Neutrons, protons,
  2564 +electrons. At the early part (before about 3 minutes in the age of the
  2565 +universe), we had too high of energy, and the neutrons plus protons could
  2566 +not form deuterium. When the temperature dropped, deuterium was able to
  2567 +form, and we had that. Then we could form Helium-3, Helium-4, etc. We have
  2568 +to be a little careful when we have two charged particles, we have a
  2569 +positive potential from the EM forces between the particles.</p>
  2570 +<p>Let me show just one thing: we can use this kind of argument to follow the
  2571 +expansion of the density of various components. In the space of a few
  2572 +moments, you are forming all of the light nuclei in the universe. Can try
  2573 +to measure amount of deuterium and whatnot. You arrive at the fact that
  2574 +ordinary matter is only a tiny part of what we observe in the universe.</p>
  2575 +<p>By the way: cosmic microwave background gives exactly the same results with
  2576 +totally different physics.</p>
  2577 +<p>Conclusion: what I wanted to conclude was the link between nuclear physics
  2578 +at small scale and the universe at large scale. Now attempting to explore
  2579 +links between particle physics / quantum gravity and the universe.</p>
  2580 +<p>Inflation: origin of small scale quantum structure.</p></div><div class='pos'></div>
2564 2581 <script src='mathjax/unpacked/MathJax.js?config=default'></script>
2565 2582 <script type="text/x-mathjax-config">
2566 2583 MathJax.Hub.Register.StartupHook("TeX Jax Ready",function () {
@@ -2593,5 +2610,4 @@
2593 2610 var div = document.getElementsByClassName('wrapper')[0];
2594 2611 div.style.width = '80%';
2595 2612 }
2596   -</script>
2597   -</div>
  2613 +</script></div>
39 phys137a.html
... ... @@ -1,4 +1,4 @@
1   -<div class='wrapper'>
  1 +<div><div class='wrapper'>
2 2 <p><a name='1'></a></p>
3 3 <h1>Physics 137A: Quantum Mechanics</h1>
4 4 <h2>Wednesday, January 18</h2>
@@ -799,7 +799,37 @@
799 799 <p>Fine-structure of hydrogen: taking into account spin interaction with
800 800 magnetic field induced by relative motion of proton (larmor precession)</p>
801 801 <p>Quadrupoles, nuclear spin, total angular momentum of electron. Angular
802   -momentum of atom: <mathjax>$I_N + \vec{J} = \vec{F}_{\mathrm{atom}}$</mathjax>.</p></div><div class='pos'></div>
  802 +momentum of atom: <mathjax>$I_N + \vec{J} = \vec{F}_{\mathrm{atom}}$</mathjax>.</p>
  803 +<p><a name='37'></a></p>
  804 +<h1>Physics 137A: Quantum Mechanics</h1>
  805 +<h1>Friday, April 27</h1>
  806 +<p>spin combinations, parity, stuff. spans space. doesn't have good symmetry
  807 +under imagined operators.</p>
  808 +<p>Annihilation of conjugate coordinates: discrete Fourier transforms and
  809 +stuff. <mathjax>$M = m_1 + m_2$</mathjax>, <mathjax>$\mu = \frac{m_1m_2}{m_1 + m_2}}$</mathjax>.</p>
  810 +<p>center of mass and stuff. Two-body problem.</p>
  811 +<p><mathjax>$\frac{1}{\Psi(R)} \frac{p^2}{2M}\Psi_{cm} = E_{cm}$</mathjax>.</p>
  812 +<p><mathjax>$\frac{1}{\Psi(r)} \parens{\frac{p^2}{2M} + \gamma} \Psi_{rel} = E_{rel}$</mathjax>.</p>
  813 +<p><mathjax>$E = E_{rel} + E_{cm}$</mathjax>.</p>
  814 +<p>Everything on the one-body problem maps directly onto the two-body
  815 +problem. There's one small difference: we can claim we're not interested in
  816 +the center-of-mass motion. We want to know the intrinsic structure, so we
  817 +can just worry about the relative motion.</p>
  818 +<p>In addition, there's spin. There are now two spins. <mathjax>$\ket{nlm; s_1m_{s1}
  819 +s_2m_{s2}}$</mathjax>.</p>
  820 +<p>Bosons and fermions. If you use separation of variables for
  821 +<mathjax>$\Psi(\vec{r_1}, \vec{r_2})$</mathjax>, what does this wave function have to look
  822 +like if we require symmetry? This wave function has probably one of two
  823 +possibilities: we exchange quantum numbers, or we introduce a minus
  824 +sign. Symmetric or antisymmetric under interchange of particle quantum
  825 +numbers.</p>
  826 +<p>Powerful theorem: depending on particle, only one is possible. Bosons: must
  827 +build symmetry under interchange. Fermions: must be antisymmetric.</p>
  828 +<p>Spin triplet state is even under particle exchange, and spin singlet is odd
  829 +under particle exchange.</p>
  830 +<p>Symmetry: can interchange. Have another spin buried in that Pauli
  831 +originally introduced. Now you have this proton neutron stuff and can just
  832 +continue.</p></div><div class='pos'></div>
803 833 <script src='mathjax/unpacked/MathJax.js?config=default'></script>
804 834 <script type="text/x-mathjax-config">
805 835 MathJax.Hub.Register.StartupHook("TeX Jax Ready",function () {
@@ -826,11 +856,10 @@
826 856 div.style.width = '15%';
827 857 for (var i = 0; i < ll; i++) {
828 858 div.innerHTML += '<a href="\#' + a[i].name + '">'
829   - + a[i].parentElement.nextElementSibling
830   - .nextElementSibling.innerText
  859 + + a[i].parentElement.nextElementSibling.innerHTML
831 860 + '</a><br />';
832 861 }
833 862 var div = document.getElementsByClassName('wrapper')[0];
834 863 div.style.width = '80%';
835 864 }
836   -</script>
  865 +</script></div>
23 sp2012/phys112/phys112.md
Source Rendered
@@ -3360,4 +3360,25 @@ for all practical purposes, does not exist.
3360 3360 Indeed, in this case, the chemical potentials add.
3361 3361
3362 3362 Problem: running out of time. Try to tell a little bit about how we discuss
3363   -the
  3363 +the formation of atoms in the early universe. Neutrons, protons,
  3364 +electrons. At the early part (before about 3 minutes in the age of the
  3365 +universe), we had too high of energy, and the neutrons plus protons could
  3366 +not form deuterium. When the temperature dropped, deuterium was able to
  3367 +form, and we had that. Then we could form Helium-3, Helium-4, etc. We have
  3368 +to be a little careful when we have two charged particles, we have a
  3369 +positive potential from the EM forces between the particles.
  3370 +
  3371 +Let me show just one thing: we can use this kind of argument to follow the
  3372 +expansion of the density of various components. In the space of a few
  3373 +moments, you are forming all of the light nuclei in the universe. Can try
  3374 +to measure amount of deuterium and whatnot. You arrive at the fact that
  3375 +ordinary matter is only a tiny part of what we observe in the universe.
  3376 +
  3377 +By the way: cosmic microwave background gives exactly the same results with
  3378 +totally different physics.
  3379 +
  3380 +Conclusion: what I wanted to conclude was the link between nuclear physics
  3381 +at small scale and the universe at large scale. Now attempting to explore
  3382 +links between particle physics / quantum gravity and the universe.
  3383 +
  3384 +Inflation: origin of small scale quantum structure.
46 sp2012/phys137a/phys137a.md
Source Rendered
@@ -1195,3 +1195,49 @@ magnetic field induced by relative motion of proton (larmor precession)
1195 1195
1196 1196 Quadrupoles, nuclear spin, total angular momentum of electron. Angular
1197 1197 momentum of atom: $I_N + \vec{J} = \vec{F}_{\mathrm{atom}}$.
  1198 +
  1199 +<a name='37'></a>
  1200 +
  1201 +Physics 137A: Quantum Mechanics
  1202 +===============================
  1203 +Friday, April 27
  1204 +================
  1205 +
  1206 +spin combinations, parity, stuff. spans space. doesn't have good symmetry
  1207 +under imagined operators.
  1208 +
  1209 +Annihilation of conjugate coordinates: discrete Fourier transforms and
  1210 +stuff. $M = m_1 + m_2$, $\mu = \frac{m_1m_2}{m_1 + m_2}}$.
  1211 +
  1212 +center of mass and stuff. Two-body problem.
  1213 +
  1214 +$\frac{1}{\Psi(R)} \frac{p^2}{2M}\Psi_{cm} = E_{cm}$.
  1215 +
  1216 +$\frac{1}{\Psi(r)} \parens{\frac{p^2}{2M} + \gamma} \Psi_{rel} = E_{rel}$.
  1217 +
  1218 +$E = E_{rel} + E_{cm}$.
  1219 +
  1220 +Everything on the one-body problem maps directly onto the two-body
  1221 +problem. There's one small difference: we can claim we're not interested in
  1222 +the center-of-mass motion. We want to know the intrinsic structure, so we
  1223 +can just worry about the relative motion.
  1224 +
  1225 +In addition, there's spin. There are now two spins. $\ket{nlm; s_1m_{s1}
  1226 +s_2m_{s2}}$.
  1227 +
  1228 +Bosons and fermions. If you use separation of variables for
  1229 +$\Psi(\vec{r_1}, \vec{r_2})$, what does this wave function have to look
  1230 +like if we require symmetry? This wave function has probably one of two
  1231 +possibilities: we exchange quantum numbers, or we introduce a minus
  1232 +sign. Symmetric or antisymmetric under interchange of particle quantum
  1233 +numbers.
  1234 +
  1235 +Powerful theorem: depending on particle, only one is possible. Bosons: must
  1236 +build symmetry under interchange. Fermions: must be antisymmetric.
  1237 +
  1238 +Spin triplet state is even under particle exchange, and spin singlet is odd
  1239 +under particle exchange.
  1240 +
  1241 +Symmetry: can interchange. Have another spin buried in that Pauli
  1242 +originally introduced. Now you have this proton neutron stuff and can just
  1243 +continue.

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