PHYSICS

Click to download source code

Here the results of a couple of MATLAB simulations I made in connection with the computational physics course (1FA573) I taugth at Uppsala University. The projects to which these simulations correspond are taken from the course book "Computational Physics" by Koonin and Meredith.

(I) THE BRUSSELATOR

In connection to project 7, in the computational physics course, here are some movies I made using MATLAB illustrating in how the concentration, X(x,y,t), of a chemical involved in the Brusselator reaction evolves through time.  Here the concentration, X, is shown as a function of the x- and y-cordinate. The color coding goes from blue (low concentration) to red (high concentration). The different examples correspond to different initial conditions. To run the movies, click on the equations below. For more details on the differential equations used to simulate this reaction see  S. Koonins Book, p. 189-194

(II) TIME DEPENDENT WAVE SCATTERING

In connection to project 7, in the computational physics course, here are some solutions to the time dependent Schrödinger equation I did in Matlab.

(1) Scattering of 1-dim gaussian wave packet by a square barrier

(2a) Scattering of 1-dim gaussian wave packet by a square well

(2b) Corresponding 2-dim example (Circular well)

(3a) Zero momentum wave packet in an infinitely deep square well

(3b) Corresponding 2-dim example (Circular well)

(4) Scattering of gaussian wave packet by 1-dim "atomic like" potential

(5) Gaussian wave packet close to the groundstate of a harmonic potential

(6) Gaussian wave packet far from the groundstate of a harmonic potential

(7a) Gaussian wave packet with finite momentum in an infinite 1-dim square well

(7b) Corresponding 2-dim example.

(8) Zero momentum gaussian wave packet in 2-dim atomic potential.

(9) Gaussian wave packet colliding with 2-dim atomic potential

(10) Lorentzian wave packet colliding with 2-dim atomic potential

(11a) Gaussian wave packet colliding with 3-dim atomic potential. Here the squared wave function is evolved in time in the Z = 0 plane.

(11b) Gaussian wave packet colliding with 3-dim atomic potential.  Here the evolution of the iso-charge density = 0.5 is shown.

(11c) Gaussian wave packet colliding with 3-dim atomic potential.  Here the evolution of the iso-charge density = 0.1 is shown.

(11d) Gaussian wave packet colliding with 3-dim atomic potential.  Here the evolution of the iso-charge density = 0.05 is shown.

(12a) Gaussian wave packet (3-dim) trapped in a box together with a coulumb potential. Here the squared wave function is evolved in time in the Z = 0 plane.

(12b) Gaussian wave packet (3-dim) trapped in a box together with a coulumb potential. Here the evolution of the iso-charge density = 0.05 is shown