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Two interacting particles in a parabolic well : harmonium and related systems

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EN
Abstrakty
EN
The quasi-exactly solvable problem of two interacting electrons confirmed by a parabolic potential (harmonium) has been generalized for the case of two arbitrary particles. Several new features of the analytical solutions are presented.
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autor
  • Institute of Physics UMK, Grudziądzka 5, 87-100 Toruń, Poland
autor
  • Institute of Physics UMK, Grudziądzka 5, 87-100 Toruń, Poland
Bibliografia
  • [1] N. R. Kestner and O. Sinanoğlu, Study of electron correlation in helium-like systems using an exactly soluble model, Phys. Rev. 128, 2687-2693 (1962).
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  • [4] M. Taut, Two electrons in an external oscillator potential: Particular analytic solutions of a Coulomb correlation problem, Phys. Rev. A48, 3561-3566 (1993).
  • [5] M. Taut and A. Ernst, Two electrons in an external oscillator potential: midtiplet splittings from exact solutions and one-particle approximations, J. Phys. B: At. Mol. Opt. Phys. 31, L35-L40 (1998).
  • [6] M. Taut, A. Ernst, and H. Eschring, Two electrons in an externa! oscillator potential: exact solutions versus one-particle approximations, J. Phys. B: At. Mol. Opt. Phys. 31, 2689-2708 (1998).
  • [7] J. Cioslowski and K. Pernal, The ground state of harmonium, J. Chem. Phys. 113, 8434-8343 (2000).
  • [8] L. Cyrnek, The energy spectrum of harmonium, in: Symmetry and Structural Properties of Condensed Matter, edited by T. Lulek. B. Lulek and A. Wal (World Scientific, Singapore. 2003).
  • [9] J. Kanvowski and L. Cyrnek. Harmonium, Ann. Phys. xx xx-xx (2004).
  • [10] P. A. Maksym and T. Chakraborty, Quantum dots in a magnetic field: Role of electron-electron interactions, Phys. Rev. Lett. 65, 108-11 1 (1990).
  • [11] U. Merkt, J. Huser, and M. Wagner, Energy spectra of two electrons in a harmonic quantum dot, Phys. Rev. B 43, 7320-7323 (1991).
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  • [14] G. Lamouche and G. Fishman, Two interacting electrons in a three-dimensional parabolic quantum dot: a simple solution, .1. Phys.: Condens. Matter 10, 7857-7867 (1998).
  • [15] A. Samanta and S. K. Ghosh. Correlation in exactly solvable two-particle quantum svslem, Phvs. Rev. A 42, 1178-1183 (1990).
  • [16] S. K. Ghosh and A. Samanta, Studv of correlation effects in an exactly solvable model two-electron system, J. Chem. Phys. 94, 517-522 (1991).
  • [17] M. Taut, Special analytical solutions of the Schrödinger equation for two and three electrons in a magnetic field and ad hoc generalizations to N particles, J. Phys.: Condens. Matter 12, 3689-3710 (2000).
  • [18] M. Taut, K. Pernal, J. Cioslowski, and V. Staemmler, Three electrons in a harmonic oscillator potential: Pairs versus single particles. J. Chem. Phys. 118, 4861-4871 (2003).
  • [19] S. K. Bose and N. Gupta. Exact solution nf nonrelativistic Schrödinger equation for certain central physical potentials, Nuovo Cimento B113, 299-32 8 (1998).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUJ8-0024-0094
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