<p>This study investigates the optical properties of two-electron quantum dots under two-dimensional parabolic confinement, selected for its analytical tractability and relevance to semiconductor heterostructures, using a Python-based computational framework. By solving the 2D Schrödinger equation with electron–electron interactions and impurity potentials, we analyze energy levels, oscillator strengths, and emission spectra. Finite-difference discretization and sparse diagonalization are employed to construct and solve the Hamiltonian matrix efficiently. We provide detailed implementation steps, parameter choices, and code-level insights to ensure reproducibility. Our results demonstrate that impurity position and charge significantly influence quantum dot spectra, enabling tunability for optoelectronic applications. Comparisons with exact diagonalization results for quantum-dot helium [Pfannkuche et al. in Phys. Rev. B 47:2244, 1993] show excellent agreement in oscillator strengths and energy levels, thereby confirming the accuracy of the framework.</p> Graphical abstract <p></p>