diff options
authorbryan newbold <>2009-06-01 19:25:19 -0400
committerbryan newbold <>2009-06-01 19:25:19 -0400
commit4d4b8c5ee17d5744b7c7f9de58c32c992c5adabd (patch)
parent48b8165eb262a538d240841c8ddb0b48761804a5 (diff)
parent1af14ac4c7de808262093c8fe0b93646ef44a34c (diff)
Merge branch 'master' of ssh://
-rw-r--r--MIT Courses9
6 files changed, 138 insertions, 5 deletions
diff --git a/MIT Courses b/MIT Courses
index 31ebaf1..4c70d7f 100644
--- a/MIT Courses
+++ b/MIT Courses
@@ -45,8 +45,8 @@ humanities concentration in philosophy.
* Spring 2008
+ **8.04** - Quantum Mechanics I (last time!)
+ **8.14** - Experimental Physics II
- + **21F.052** - French Film Classics (spring, in english)
- + **18.100b** - Analysis
+ + **21F.052** - French Film Classics
+ + **18.100b** - Analysis I
* Fall 2008
+ **8.05** - Quantum Mechanics II
@@ -56,10 +56,8 @@ humanities concentration in philosophy.
* Spring 2009 (planned)
+ 8.06 - Quantum Mechanics III
- + 8.962 - General Relativity
+ 6.945 - Adventures in Symbolic Programming
+ 4.602 - Modern Art and Mass Culture
- + 8.ThU - Thesis
Other interesting courses:
+ 24.215 - Topics in the Philosophy of Science (fall)
@@ -81,5 +79,6 @@ Other interesting courses:
+ 8.371J - Quantum Information Science (grad, spring)
+ 8.594J - Introduction to Neural Networks (grad, fall)
+ 8.284 - Modern Astrophysics (spring)
- + 8.942 - Cosmology (grad, spring)
+ + 8.942 - Cosmology (grad, fall)
+ + 8.962 - General Relativity (grad, spring)
diff --git a/physics/quantum/fermigas b/physics/quantum/fermigas
new file mode 100644
index 0000000..0114b43
--- /dev/null
+++ b/physics/quantum/fermigas
@@ -0,0 +1,51 @@
+Fermi Gas
+Derivation of the Fermi Energy
+Consider a crystal lattice with an electron gas as a 3 dimensional infinite
+square well with dimensions :m:`$l_{x}, l_{y}, l_z$`. The wavefunctions of
+individual fermions (pretending they are non-interacting) can be seperated
+as :m:`$\psi(x,y)=\psi_{x}(x)\psi_{y}(y)\psi_{z}(z)$`. The solutions will be
+the usual ones to the Schrodinger equation:
+:m:`$$\frac{-\hbar^2}{2m}\frac{d^2 \psi_x}{dx}=E_x \psi_x$$`
+with the usual wave numbers :m:`$k_x=\frac{\sqrt{2mE_x}}{\hbar}$`, and quantum
+numbers satisfying the boundry conditions :m:`$k_x l_x = n_x \pi$`. The full
+wavefunction for each particle will be:
+and the associated energies (with :m:`$E = E_x + E_y + E_z$`):
+where :m:`$|\vec{k}|^2$` is the magnitude of the particle's k-vector in k-space.
+This k-space can be imagined as a grid of blocks, each representing a possible
+particle state (with a double degeneracy for spin). Positions on this grid have
+coordinates :m:`$(k_{x},k_{y},k_z)$` corresponding to the positive integer
+quantum numbers. These blocks will be filled
+from the lowest energy upwards: for large numbers of occupying particles,
+the filling pattern can be approximated as an expanding spherical shell with
+radius :m:`$|\vec{k_F}|^2$`.
+Note that we're "over counting" the number of occupied states because the
+"sides" of the quarter sphere in k-space (where one of the associated quantum
+numbers is zero) do not represent valid states. These surfaces can be ignored
+for very large N because the surface area to volume ratio is so low, but the
+correction can be important. There will then be a second correction due to
+removing the states along the individual axes twice (once for each
+side-surface), u.s.w.
+The surface of this shell is called the Fermi surface and represents the most
+excited states in the gas. The radius can be derived by calculating the total
+volume enclosed: each block has volume :m:`$\frac{\pi^3}{l_x l_y
+l_z}=\frac{\pi^3}{V}$` and there are N/2 blocks occupied by N fermions, so:
+:m:`$$\frac{1}{8}(\frac{4\pi}{3} |k_{F}|^{3})&=&\frac{Nq}{2}(\frac{\pi^{3}}{V})\\|k_{F}|&=&\sqrt{\frac{3Nq\pi^2}{V}}^3=\sqrt{3\pi^2\rho}^3$$`
+:m:`$\rho$` is the "free fermion density". The corresponding energy is:
+:m:`$$E_{F}=\frac{\hbar^{2}}{2m}|k_{F}|^{2}=\frac{\hbar^{2}}{2m}(3\rho \pi)^{2/3}$$`
diff --git a/physics/units b/physics/units
new file mode 100644
index 0000000..b1968f4
--- /dev/null
+++ b/physics/units
@@ -0,0 +1,53 @@
+.. contents::
+SI Units
+The SI system uses meters-kilograms-seconds. It also defines the Coulomb as
+a unit for measuring electric charge, which introduces redundant conversions
+between mass-length-time units and the electric charge.
+cgs Units
+The cgs system uses centimeters-grams-seconds, and also defines electric charge
+in terms of the fundamental quantities of mass, length, and time. The unit of
+charge is "esu" or electrostatic unit.
+Natural Units
+Natural units are a system of units which replace (or re-scale) the usual mass,
+length, and time bases with quantities which have "natural" (physical)
+constants associated with them. The two constants usually chosen are the speed
+of light (c) and Plank's constant (:m:`$\hbar$`); the gravitational constant
+(G) is a possibility for the third constant/unit, but energy (in
+electron-volts: eV) is often used instead because it gives more useful
+relations and because there is no accepted theory of quantum gravity to unite
+these three constants. See _`Plank Units` for more on using G as a unit.
+Working with natural units simplifies physical relations and equations because
+many conversion factors drop out.
+Given the relations between cgs units (gm, cm, sec) and natural units (c,
+:m:`$\hbar$` , eV), we can find the natural units of an arbitrary quantity
+:m:`$$(\alpha,\beta,\gamma)=\left(\begin{array}{ccc} -2 & 1 & 0\\ 0 & 1 & 1\\ 1 & -1 & -1\end{array}\right)\left(\begin{array}{c} a\\ b\\ c\end{array}\right)=(-2a+b,b+c,a-b-c)$$`
+or in reverse:
+:m:`$$(a,b,c)=\left(\begin{array}{ccc} 0 & 1 & 1\\ 1 & 2 & 2\\ -1 & -1 & -2\end{array}\right)\left(\begin{array}{c} \alpha\\ \beta\\ \gamma\end{array}\right)=(\beta+\gamma,\alpha+2\beta+\gamma,-\alpha-\beta-2\gamma)$$`
+Plank Units
+Plank units (defined by Plank soon after defining his constant :m:`$\hbar$`) are a version of _`Natural Units` using the gravitational constant G as the the
+third unit (instead of the common measure of energy). When converted back into
+mass-length-time units we get three quantities which define the "Plank Scale",
+which may provide estimation of the domain where quantum gravity effects become
+important (similar to how the speed of light and Plank's constant provide
+estimation of when special relativistic and quantum mechanical effects become
diff --git a/software/freebsd-tricks b/software/freebsd-tricks
index 84010f6..0344abd 100644
--- a/software/freebsd-tricks
+++ b/software/freebsd-tricks
@@ -7,3 +7,8 @@ Burn an ISO image
To burn a CD-R, use ``burncd`` like so::
$ burncd -f /dev/acd0 data FILENAME.iso fixate
+Network Tools
+``iftop`` is great.
diff --git a/software/gimp b/software/gimp
new file mode 100644
index 0000000..97d7393
--- /dev/null
+++ b/software/gimp
@@ -0,0 +1,19 @@
+The Gimp
+How to Sharpen Photos
+First decompose the image into HSV: Colors/Compose.../Decompose. Select
+"HSV" from the list and "Decompose to Layers". This will make a new image
+(close the original).
+Select the "Value" layer for editing (so that colors aren't affected). The
+"Unsharped Mask" filter is under Filters/Enhance.
+Radius is how many pixels to select, amount is the strength of the filter,
+and threshold allows parts of the image to be ignored.
+After applying the filter go back to Colors/Compose.../Compose and select
+HSV again to regenerate the color image.
diff --git a/software/scheme b/software/scheme
index c64d000..dda68f1 100644
--- a/software/scheme
+++ b/software/scheme
@@ -77,3 +77,9 @@ image can be specified with the ``--band`` option at runtime or with
``(disk-restore filename)`` from within the interpreter. Bands are also called
+"First Class"
+"Procedures as first class objects" is one of the features commonly attributed
+to scheme. What does that mean? SICP describes first class objects as those
+that can be: named by variables, passed as arguments, returned as results,
+and included in data structures.