Griesemer, Marcel; Lieb, Elliott H.; Loss, Michael Ground states in non-relativistic quantum electrodynamics. (English) Zbl 1044.81133 Invent. Math. 145, No. 3, 557-595 (2001). Hydrogen atom is not an exactly solvable quantum mechanical sytem if radiative processes are taken into account. The authors formulated quite generally the problem of non-relativistic quantum mechanics taking into account radiation and give some exact results. Previously the similar, but most restricted poblem, was examined by Arai and coauthors (1983-1999). The authors of the actual paper show the occurence of a ground state (of a state with minimum of the energy), which satisfies the Schrödinger equation for all values of the particle mass, the fine-structure constant, the magnetic g-factor and the ultraviolet cutoff. An important question arises in the connection with the problem examined: for which concrete values of the N’ the problem can be solved exactly? This could be usseful in concrete quantum electrodynamical calculations. Reviewer: Alex Gaina (Chisinau) Cited in 2 ReviewsCited in 113 Documents MSC: 81V10 Electromagnetic interaction; quantum electrodynamics 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis 81V70 Many-body theory; quantum Hall effect Keywords:quantum electrodynamics; non-relativistic approach; many-body systems; external fields; radiation; ground states; bound states; ultraviolet cutoff PDFBibTeX XMLCite \textit{M. Griesemer} et al., Invent. Math. 145, No. 3, 557--595 (2001; Zbl 1044.81133) Full Text: DOI arXiv