I have a few demonstrations that I made while I was learning coding during my undergrad studies. Some more interesting demonstrations that I worked out as part of other projects are also listed. Maybe you will find one of them helpful or illuminating.
Neutrino Oscillations : A very basic demo on plotting analytical functions representing neutrino oscillations, but from a quantum mechanics perspective, without too much detail on the high-energy physics behind it. To put it briefly, neutrinos come in three flavors: electron-, muon- and tau-neutrinos, corresponding to the three generations of leptons. One of these can convert to the other via weak couplings in the standard model, the reason for these conversions being that the flavor states are not eigenstates of the mass. I show how the neutrino oscillation scenario changes when the initial state is either an electron-neutrino, a muon-neutrino or a tau-neutrino. Code can be found here (Jupyter Notebook). I also have a few slides on the topic, describing the work done in the code. Slides can be found here
Intermediate Axis Theorem : Another basic demo on the Intermediate Axis Theorem in Classical Mechanics. A general object (for example, a tennis racket) has three principal axes of rotation. Rotation about the axis with the smallest or the largest moment of inertia is stable, while that about the axis with intermediate moment of inertia (hence the name, intermediate axis) is unstable with respect to small perturbations along the other axes. This is also famously known as the ‘Tennis Racket Theorem’. The code can be found here (Mathematica Notebook)
Character Table : A useful concept in finite group theory is the calculation of character tables, which hold the characters (or traces) of the various irreducible representations of the group. One can read off various properties of a group simmply from the character table, such as which symmetries/transformations are represented by a group element, or which basis objects (such as basis vectors) correspond to a particular representation of the group. However, computing character tables from scratch is difficult. In my code, I show how the character table can be computed using basic principles of orthogonality. An example code can be found here (Mathematica Notebook). Also see other notebooks in the folder for more examples. This and the next demonstration are part of the publication arXiv:2408.01441 [physics.ed-ph]
Clebsch-Gordan coefficients : In the theory of compact groups, one often encounters Clesbch-Gordan coefficients which connect the basis of a direct product group with those of the factors. For example, a well-known such product is the tensorial relation \(\frac{1}{2}\otimes\frac{1}{2}=0\oplus 1\) for the SU(2) Lie algebra, which depicts how the addition of two spin-half (spinor) representations of the spin algebra gives rise to a scalar and a vector representation. I show how these spin-additions can be understood in terms of matrix representations, and how the Clebsch-Gordan coefficients arise from a transformation between two matrices. The code can be found here