Editorial: Recent mathematical and theoretical progress in quantum mechanics

foundations remains essential for further advances in both fundamental science and emerging quantum and mathematical physics that share common tools and perspectives when applied to quantum systems.The articles in this collection reflect several complementary directions of current research in quantum 13 mechanics and illustrate the breadth of this endeavor. Broadly speaking, they address structural aspects of 14 quantum theory through functional analysis and spectral theory, the role of point interactions and singular 15 perturbations in quantum Hamiltonians, the analysis of relativistic quantum models, and applications of 16 these ideas in condensed-matter systems and quantum field-theoretic dynamics. These contributions are 17 briefly described below.Focusing on structural aspects of quantum mechanics from the perspective of functional analysis and thereby contributing to the relatively small set of quantum systems for which completeness relations can be 29 rigorously established in explicit form.Point interactions provide analytically tractable models in quantum mechanics and are generally viewed 31 as ideal models approximating real short-range interactions. Fundamental spectral and scattering properties 32 of quantum systems can be investigated in detail in such models. In this context, Golovaty and Hryniv 33 (2025) examine the spectral properties of one-dimensional Schrödinger operators with δ -type perturbations.Studying a sequence of regularized Hamiltonians approximating these interactions, the authors show that 35 although the operators converge in the norm-resolvent sense to a semi-bounded limit, the approximating 36 sequence may nonetheless contain arbitrarily many negative eigenvalues diverging to minus infinity in the