Modern digital system cameras and also some digital compact cameras allow to create and to store images in a so-called raw format. A raw image contains the minimally pre-processed sensor data, meta-data about the picture such as camera model, lens model and camera settings under which the picture has been taken and possibly a fully… Continue reading From numbers to images – Raw image processing with Python
Computing the eigenvectors $\psi(x)$ and eigenvalues $E$ of some Hamiltonian $H$ belongs to the key problems of quantum mechanics. For the one-dimensional Schrödinger equation we have to solve \begin{equation} E\psi(x) = H\psi(x) = -\frac{1}{2}\frac{\mathrm{d}^2\psi(x)}{\mathrm{d} x^2} + V(x)\psi(x) \end{equation}for some given potential $V(x)$. Analytical solutions, however, are scare goods. Thus, one has to rely on approximations… Continue reading Eigenvalues and eigenfunctions
In Visualizing vector fields I showed how to plot vector fields using Python and Matplotlib. Streamlines are a concept that is closely related to vector fields. Mathematically speaking streamlines are continuous lines whose tangent at each point is given by a vector field. Each line, and therefore also streamlines, can be parametrized by some parameter $t$.… Continue reading Visualizing streamlines
A vector field assigns to every point in space some vector. Vector fields are used in many branches of physics, e.g., to describe force fields, electromagnetic fields or velocity fields. Two-dimensional vector fields can be easily visualized using Python and the popular matplotlib package. As an example let us visualize the vector field \begin{equation} \vec… Continue reading Visualizing vector fields
Let us consider a random sample $x_1,x_2,\dots,x_N$ drawn from a normal distribution with unknown mean $\mu$ and unknown variance $\sigma^2$. The best point estimates for the mean and the variance are given by the sample mean\begin{equation} \hat\mu = \frac{1}{N}\sum_{i=1}^{N} x_i \end{equation} and the sample variance \begin{equation} \hat\sigma^2 = \frac{1}{N-1}\sum_{i=1}^{N} (x_i-\hat\mu)^2\,, \end{equation} respectively. The sample mean… Continue reading Point and interval estimation in Python
From time to time students ask me what might be the best programming language for computational physics and numerical applications. For a long time my standard answer to this question was twofold: The language does not matter, learn C++! On the one hand, I think one should not bother to much with this issue because… Continue reading Scientific Python