Eikonal Blog

2010.07.13

TeX and LaTeX links

Filed under: TeX — Tags: , , , , , , , , , , — sandokan65 @ 16:03

Tools


(to be a) Cheatsheet

Lists

    \begin{list}{label code}{body code}
    \item Item one
    \item Item two
    \item Item three
    \end{list}
    

Example:

    \begin{list}{*}{}
    \item Item one
    \item Item two
    \item Item three
    \end{list}
    

Error: “extra alignment tab has been changed to \cr” in pmatrix environment

Trying to compile the matrix with 16 columns:

    $$
    \begin{pmatrix}
    1&0&0&0& 0&0&0&0& 0&1&0&0& 0&0&0&0 \\
    0&0&0&0& 1&0&0&0& 0&0&0&0& 0&1&0&0 \\
    0&0&1&0& 0&0&0&0& 0&0&0&1& 0&0&0&0 \\
    0&0&0&0& 0&0&1&0& 0&0&0&0& 0&0&0&1
    \end{pmatrix}
    $$
    

produced following error:

    ./document.tex:750: Extra alignment tab has been changed to \cr.
     \endtemplate
    
    l.750 1&0&0&0& 0&0&0&0& 0&1&
                                0&0& 0&0&0&0 \\
    

It appears that LaTeX has some internal limitation on default maximal number of columns. This can be changed (accoring to http://newsgroups.derkeiler.com/Archive/Comp/comp.text.tex/2006-06/msg01298.html) by setting

    \setcounter{MaxMatrixCols}{16}
    

in the preamble of the document.

2010.03.28

Physics books online

Filed under: books, physics — Tags: , , , , — sandokan65 @ 15:03

Related at this blog: Physics sites – https://eikonal.wordpress.com/2010/02/12/physics-sites/ | Books online – https://eikonal.wordpress.com/2010/01/04/books-online/ | Mathematics sites (go to Books section)- https://eikonal.wordpress.com/2010/03/17/mathematics-sites/ | Expand your mind – https://eikonal.wordpress.com/2010/01/04/expand-your-mind/

2010.03.19

Energy Scales in Physics

Filed under: physics — Tags: , — sandokan65 @ 10:39

The Physics Department at Princeton University has a nice map of energy scales currently known to physics: https://www.princeton.edu/physics/research/high-energy-theory/gubser-group/introduction-to-the-physi/energy-scales-in-physics/.

2010.02.12

Physics sites

Physics seminars

Collections of historic papers


Physics blogs

Physics wikis

  • SklogWiki – sklogwiki.org – dedicated to the thermodynamics of simple liquids, complex fluids, and soft condensed matter
  • Qwiki – qwiki.stanford.edu – a quantum physics wiki devoted to the collective creation of technical content for practicing scientists
  • Quantiki – quantiki.org – dedicated to the quantum information science

Astronomy and Astrophysics

Related here:

Complexity (Integrability, Exact Solvability, Chaos, Small Worlds, Networking, etc)

Various

Related information on this blog

2010.01.24

Heat conduction equation

Filed under: physics — Tags: — sandokan65 @ 23:38

The problem is defined by following three elements:

  • ODE: \partial_t u = k \partial_x^2 u,
  • Domain: D=\{(x,t)|x\in{\Bbb R}, t\in{\Bbb R}^{+}\},
  • Initial condition: u(x,0)=f(x).

Using the Fourier transform one gets to the solution:
u(x,t) = \frac1{(2\pi)^\mu} \int_{\Bbb R} e^{-ipx-kp^2t}{\bf F}[f](p).

For example, for f(x)=A e^{-Bx^2} one gets u(x,t) = \frac{A}{\sqrt{1+4Bkt}} e^{-\frac{Bx^2}{1+4Bkt}}.

2010.01.04

Harmonic oscillator

Filed under: Quantum mechanics — Tags: , , — sandokan65 @ 20:23

Potential function: U(x)=\frac{m\omega^2 x^2}{2}

Solutions of the Schr\”odinger equation:

  • States: \psi_n(x) = (\frac{m}{\hbar\omega})^{\frac14}  \frac{1}{\sqrt{2^n n! \pi}} H_n(\sqrt{\frac{m\omega}{\hbar}}x) e^{-\frac{m\omega x^2}{\hbar}}
  • Energies: E_n=\hbar\omega (n+\frac12)

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