schroedingerSolver – numerical solutions of Schrödinger’s equation (stationary case)

You can feed an arbitrary one-dimensional potential into the solver, along with information about the observed interval and discretisation. The program interpolates the potential and solves Schrödinger’s equation numerically in order to obtain an arbitrary number of wave functions, as well as their corresponding energy levels. All of the results are broken up in output files which can easily be displayed graphically. Additionally, a Matlab routine is provided for the purpose of obtaining a neat plot of the results. The program SchroedingerSolver is written entirely in Fortran and uses several LAPACK routines.

This program was co-authored by Andreas Krut. We used the distributed revision control system bazaar(bzr) in order to revise and merge our code.

In the readme (see below) you’ll find detailed instructions on how to compile and run the program, as well as all the necessary prequisites. If you have already set up your workspace, you can make a test compile via

>$ make test_lite

schroedingerSolver_output

The documentation should give a good idea of how the program works. Also, visit the schroedingerSolver Launchpad developer site, or download a zip file of the repo directly.

 

Animated Lagrange Top

This Matlab programme simulates a Lagrange top, which is a symmetric top spinning in a gravitational field. To call it, type

kreisel([1,10],[0;pi;pi/2;0;0;0])

The first parameter is a time interval \([t_0,t_\text{end}]\) and the second parameter are the initial conditions of the Euler angles \([\varphi,\dot{\varphi},\vartheta,\dot{\vartheta},\psi,\dot{\psi}]\).

The spinning top zip folder contains the code, typed documentation and a Mathematica notebook in which I derive the ordinary differential equations which are solved numerically in Matlab.

Fast Fourier Transformation

Die zwei Programme fftw4.c und fftwd2.c binden die FFTW-Programmbibliothek ein (“Fastest Fourier Transform in the West”). Die Programme führen FFT-Transformationen durch und zeigen einigeAnwendungsbeispiele auf, bei denen die numerische Fourier-Trnasformation zum Einsatz kommt. fftw4.c transformiert eine gegebene

Funktion vom Originalbereich in den Fourier-Bereich, was anhand von Gauss-Kurve,verschiedenen Spalten und einem Gitter gezeigt wird (siehe Bild).

fftwd2.c vergleicht unterschiedliche Methoden des numerischen Differenzierens und zeigt den Vorteil des Differenzierens im Fourier-Raum auf. Beide C-Programme sind in der Dokumentation ausführlich beschrieben.

Interferenzmuster

fftw4.c

fftwd2.c

Dokumentation