Study of a hydrogenic atom near a rigid wall by using the finite element method
Literature Information
Juan David Serna-Salazar, Jorge Mahecha-Gómez
A direct numerical solution of the Schrödinger equation for a hydrogenic atom near a rigid wall, and the corresponding graphics of some of the energies and wave functions are presented. The solution is obtained by using the finite-element method (FEM) with the appropriate boundary conditions. In particular, crossings of the von Neumann–Wigner type are observed and a classification is suggested of different eigenenergy sets, according to symmetries of the system. The limit with the nucleus being on the wall and the 3D bulk limit are also studied. A discussion of a possible role of the model for the treatment of atom–surface interactions is presented. This system can also be used as a model for 2D and 3D quantum devices, such as shallow state of impurity atoms or Wannier exciton near interfaces.
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Physical Chemistry Chemical Physics

Physical Chemistry Chemical Physics (PCCP) is an international journal co-owned by 19 physical chemistry and physics societies from around the world. This journal publishes original, cutting-edge research in physical chemistry, chemical physics and biophysical chemistry. To be suitable for publication in PCCP, articles must include significant innovation and/or insight into physical chemistry; this is the most important criterion that reviewers and Editors will judge against when evaluating submissions. The journal has a broad scope and welcomes contributions spanning experiment, theory, computation and data science. Topical coverage includes spectroscopy, dynamics, kinetics, statistical mechanics, thermodynamics, electrochemistry, catalysis, surface science, quantum mechanics, quantum computing and machine learning. Interdisciplinary research areas such as polymers and soft matter, materials, nanoscience, energy, surfaces/interfaces, and biophysical chemistry are welcomed if they demonstrate significant innovation and/or insight into physical chemistry. Joined experimental/theoretical studies are particularly appreciated when complementary and based on up-to-date approaches.














