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Ground states in non-relativistic quantum electrodynamics. (English) Zbl 1044.81133

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.

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
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