Abstract:
Sufficient conditions are found of the finiteness of discrete spectrum of energy
operators (in terms of the coordinate and momentum representation) in the symmetry
spaces for many-particle systems for which the boundary of continuous spectrum of the
Hamiltonian is determined by the dividing into two stable subsystems. In particular,
molecules, negative ions of any atoms and systems with short-range interactions are
considered. For the systems under consideration the results obtained generalize those
known earlier.
Citation:
S. A. Vugal'ter, G. M. Zhislin, “Finiteness of the discrete spectrum of many-particle Hamiltonians in symmetry spaces”, TMF, 32:1 (1977), 70–87; Theoret. and Math. Phys., 32:1 (1977), 602–614
\Bibitem{VugZhi77}
\by S.~A.~Vugal'ter, G.~M.~Zhislin
\paper Finiteness of the discrete spectrum of many-particle Hamiltonians in symmetry spaces
\jour TMF
\yr 1977
\vol 32
\issue 1
\pages 70--87
\mathnet{http://mi.mathnet.ru/tmf3137}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=449304}
\transl
\jour Theoret. and Math. Phys.
\yr 1977
\vol 32
\issue 1
\pages 602--614
\crossref{https://doi.org/10.1007/BF01041434}
Linking options:
https://www.mathnet.ru/eng/tmf3137
https://www.mathnet.ru/eng/tmf/v32/i1/p70
This publication is cited in the following 21 articles:
Mathieu Lewin, Mathématiques et Applications, 87, Théorie spectrale et mécanique quantique, 2022, 221
Simon B., “Tosio Kato'S Work on Non-Relativistic Quantum Mechanics, Part 2”, Bull. Math. Sci., 9:1 (2019), UNSP 1950005
Brian T. Sutcliffe, “An analysis of the role of the Born–Oppenheimer approximation in calculating rotational–vibrational interactions in molecules”, Theor Chem Acc, 130:2-3 (2011), 187
Brian T. Sutcliffe, “What mathematicians know about the solutions of Schrodinger Coulomb Hamiltonian. Should chemists care?”, J Math Chem, 44:4 (2008), 988
Brian T. Sutcliffe, R. Guy Woolley, “Molecular structure calculations without clamping the nuclei”, Phys. Chem. Chem. Phys., 7:21 (2005), 3664
Brian Sutcliffe, “Some observations on P.‐O. Löwdin's definition of a molecule”, Int J of Quantum Chemistry, 90:1 (2002), 66
W. Hunziker, I. M. Sigal, “The quantum N-body problem”, Journal of Mathematical Physics, 41:6 (2000), 3448
Brian Sutcliffe, Advances in Chemical Physics, 114, Advances in Chemical Physics, 2000, 1
Brian T. Sutcliffe, Lecture Notes in Chemistry, 71, Potential Energy Surfaces, 1999, 61
S. A. Vugal'ter, G. M. Zhislin, “The Discrete Spectrum of a Many-Particle Pseudorelativistic Hamiltonian”, Funct. Anal. Appl., 32:2 (1998), 134–136
Brian T. Sutcliffe, Fundamental Principles of Molecular Modeling, 1996, 11
Brian T. Sutcliffe, “The idea of a potential energy surface”, Journal of Molecular Structure: THEOCHEM, 341:1-3 (1995), 217
Volker Bach, Roger Lewis, Elliott H. Lieb, Heinz Siedentop, “On the number of bound states of a bosonicN-particle Coulomb system”, Math Z, 214:1 (1993), 441
W. D. Evans, Roger T. Lewis, Yoshimi Saitò, “Zhislin's theorem revisited”, J. Anal. Math., 58:1 (1992), 191
S. A. Vugal'ter, “Asymptotic behavior of the eigenvalues of many-particle Hamiltonians on subspaces of functions of a given symmetry”, Theoret. and Math. Phys., 83:2 (1990), 502–510
S. A. Vugal'ter, G. M. Zhislin, “On finiteness of the discrete spectrum of the energy operators of multiatomic molecules”, Theoret. and Math. Phys., 55:1 (1983), 357–365
S. A. Vugal'ter, G. M. Zhislin, “On the discrete spectrum of the energy operator of one- and two-dimensional quantum three-particle systems”, Theoret. and Math. Phys., 55:2 (1983), 493–502
I. M. Sigal, “Geometric methods in the quantum many-body problem. Nonexistence of very negative ions”, Commun.Math. Phys., 85:2 (1982), 309
I. M. Sigal, Lecture Notes in Physics, 153, Mathematical Problems in Theoretical Physics, 1982, 149
Mary Beth Ruskai, “Absence of discrete spectrum in highly negative ions”, Commun.Math. Phys., 82:4 (1982), 457
Citation in format AMSBIB
Contact us: