Jupyter notebooks for the lecture using numerical concepts for propagtion of physical systems in time and calculation of eigenenergiesm and other expectation values.
All notebooks work with the following package-versions:
Package | Version |
---|---|
python | 3.9 |
numpy | 1.22.2 |
scipy | 1.7.3 |
matplotlib | 3.3.4 |
ipython | 7.30.1 |
ipympl | 0.2.1 |
Propagation of atomic wavefunctions using the Multiphoton-Matrix-Iterative-Method on non-uniform grids. We use atomic units. The hamiltonian operator reads
$$ \hat{H}0\Psi{\ell}(r, t)Y_{\ell,m}(\theta,\varphi) = \left(-\frac{1}{2 r^2}\frac{\partial}{\partial r}\left(r^2 \frac{\partial}{\partial r} \Psi_{\ell}(r, t) \right) + \frac{\ell(\ell+1)}{2r^2}\Psi_{\ell}(r, t) - \frac{1}{r}\Psi_{\ell}(r, t)\right) Y_{\ell,m}(\theta,\varphi).$$
Artificial one-dimensional atom of the form
Generic two-level system subjected to an external classical field is described via the hamiltonian
Calculations of various expectation values like magnetization and susceptibility