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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

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

Citations:

Zbl 0774.47040
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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
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