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In this article, we describe an approach to teaching introductory quantum mechanics and machine learning techniques. This approach combines several key concepts from both fields. Specifically, it demonstrates solving the Schrödinger equation using the discrete-variable representation (DVR) technique, as well as the architecture and training of neural network models. To illustrate this approach, a Python-based Jupyter notebook is developed. This notebook can be used for self-learning or for learning with an instructor. Furthermore, it can serve as a toolbox for demonstrating individual concepts in quantum mechanics and machine learning and for conducting small research projects in these areas. 

Dissociative recombination of the OH+ ion with free electrons is modeled theoretically using a recently developed approach that is based on first-principles calculations and multichannel quantum defect theory. The coupling between the incident electron and the rovibrational motion of the ion is accounted for. The cross section of the process at collision energies 10−6–1 eV and the thermally averaged rate coefficient at 10–1000 K are evaluated. The obtained anisotropic rate coefficients agree well with the data from a recent experiment carried out at the Cryogenic Storage Ring, especially when compared to previous theoretical values, which are smaller than the experimental results by about a factor of about 30. 

Cross sections and thermally averaged rate coefficients for the vibrational excitation and de-excitation by electron impact on the HDO molecule are computed using a theoretical approach based entirely on first principles. This approach combines scattering matrices obtained from the UK R-matrix codes for various geometries of the target molecule, three-dimensional vibrational states of HDO, and the vibrational frame transformation. The vibrational states of the molecule are evaluated by solving the Schrödinger equation numerically, without relying on the normal-mode approximation, which is known to be inaccurate for water molecules. As a result, couplings and transitions between the vibrational states of HDO are accurately accounted for. From the calculated cross sections, thermally averaged rate coefficients and their analytical fits are provided. Significant differences between the results for HDO and H2O are observed. Additionally, an uncertainty assessment of the obtained data is performed for potential use in modeling non-local thermodynamic equilibrium (non-LTE) spectra of water in various astrophysical environments. 

This study presents Born–Oppenheimer energies and transition dipole moments of the 36 lowest electronic states of the N2+ ion as a function of internuclear distance in the interval between 1.5 and 10 bohrs obtained in first-principles calculations. The electronic states are of the total electronic spin S = 1/2, 3/2, and 5/2, dissociating toward to the lowest four N(4S0) + N+(3P), N(2P0) + N+(3P), N(2D0) + N+(3P), and N(4S0) + N+(1D) dissociation limits. Energies of the lowest states, dissociating toward to the N(4S0) + N+(3P) limit, are computed accounting for relativistic corrections. The obtained potential energy curves and the transition dipole moments are employed to compute vibrational energies in these states, vibronic transition dipole moments, and the Einstein coefficients for radiative transitions between the vibronic levels.