Vugal’ter, S. A.; Zhislin, G. M. On the discrete spectrum of the given \(\mathrm{SO}(2)\) symmetry of multiparticle systems in potential field homogeneous magnetic fields. (English. Russian original) Zbl 0830.47051 J. Math. Sci., New York 75, No. 6, 2002-2010 (1995). Translation from Zap. Nauchn. Semi. POMI 197, 28–41 (Russian) (1992; Zbl 0774.47040). MSC: 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis 81V10 Electromagnetic interaction; quantum electrodynamics 47N50 Applications of operator theory in the physical sciences Keywords:rotational symmetry; identical particles in a homogeneous magnetic field; discrete spectrum of the Hamiltonian; permutational symmetry; asymptotics Citations:Zbl 0774.47040 PDFBibTeX XMLCite \textit{S. A. Vugal'ter} and \textit{G. M. Zhislin}, J. Math. Sci., New York 75, No. 1, 28--41 (1992; Zbl 0830.47051) Full Text: DOI References: [1] S. N. Solnyshkin, ”On the discrete spectrum of a quantum particle in electric and homogeneous magnetic fields,”Algebra Analiz,3, No. 6 (1991). · Zbl 0762.35074 [2] S. A. Vugal’ter and G. M. Zhislin, ”Asymptotics of the discrete spectrum of Hamiltonians of a multiparticle quantum system in a homogeneous magnetic field,”Algebra Analiz,3, No. 6 (1991). · Zbl 0791.47058 [3] J. E. Avron, I. W. Herbst, and B. Simon, ”Schrödinger operators with magnetic field III. Atoms in homogeneous magnetic fields,”Comm. Math. Phys. 79, 529–572 (1984). · Zbl 0464.35086 · doi:10.1007/BF01209311 [4] S. A. Vugal’ter and G. M. Zhislin G.M., ”On the discrete spectrum of negative hydrogen ion with homogeneous magnetic field,”Lett. Math. Phys. [5] G. M. Zhislin, ”The finiteness of the discrete spectrum in the N-particle quantum problem,”Teor. Mat. Fiz.,21, 60–73 (1974). [6] J. E. Avron, I. W. Herbst, and B. Simon, ”Schrödinger operators with magnetic field. I. General interactions”Duke Math. J.,45, 847–883 (1979). · Zbl 0399.35029 · doi:10.1215/S0012-7094-78-04540-4 [7] S. A. Vugal’ter and G. M. Zhislin, ”The finiteness of the discrete spectrum in the N-particle problem,”ROMP,19, 34–90 (1984). · Zbl 0581.46063 [8] S. A. Vugal’ter and G. M. Zhislin, ”Asymptotics of the discrete spectrum of Hamiltonians of quantum systems with homogeneous magnetic field,” Oper. Theory,Adv. Appl.,46, 33–53 (1990). · Zbl 0731.47016 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.