New Method for Solving Three-Dimensional Schroedinger Equation

  • V. S. Melezhik
Conference paper
Part of the Few-Body Systems book series (FEWBODY, volume 6)


A new method is developed for solving the multidimensional Schroedinger equation without the variable separation. To solve the Schroedinger equation in a multidimensional coordinate space X, a difference grid Ω i (i=1,2,...,N) for some of variables ,Ω, from X = {R, Ω} is introduced and the initial partial-differential equation is reduced to a system of N differential-difference equations in terms of one of the variables R. The arising multi-channel scattering (or eigen-value) problem is solved by the algorithm based on a continuous analog of the Newton method. The approach has been successfully tested for several two-dimensional problems (scattering on a nonspherical potential well and ”dipole” scatterer, a hydrogen atom in a homogeneous magnetic field) and for a three-dimensional problem of the helium-atom bound states.


Variable Separation Homogeneous Magnetic Field Continuous Analog Difference Grid Schroedinger Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    V.S. Melezhik, J. Comp. Phys. 92 (1991) 67.ADSMATHCrossRefGoogle Scholar
  2. [2]
    J.V. Lill, G.A. Parker and J.C. Light, Chem.Phys.Lett., 89 (1982)483ADSCrossRefGoogle Scholar
  3. J.C. Light, I.P. Hamilton and J.V. Lill, J. Chem. Phys., 82 (1985)1400.ADSCrossRefGoogle Scholar
  4. [3]
    W. Yang and A.C. Peet, Chem.Phys. Lett., 153 (1988) 98.ADSCrossRefGoogle Scholar
  5. [4]
    R.A. Freisner, Chem.Phys.Lett., 118 (1985)39.ADSCrossRefGoogle Scholar
  6. [5]
    V.S. Melezhik, J. Comp. Phys., 85 (1986) 1.ADSCrossRefGoogle Scholar
  7. [6]
    S.K. Godunov and V.S. Rjabenky, Difference Schemes,Nauka,Moscow, 1977(In Russian).Google Scholar
  8. [7]
    V.S. Melezhik, Nuovo Cimento B108 (1991) 37.Google Scholar
  9. [8]
    I.S. Berezin and N.P. Zhidkov, Numerical Methods (in Russian) vi, Nauka (Moscow, 1959 ).Google Scholar
  10. [9]
    F.S. Levin and J. Shertzer, Phys.Rev. A32 (1985) 3285.ADSGoogle Scholar
  11. [10]
    I.L. Hawk and D.L. Hardcastl, Comput.Phys.Commun. 18 (1979) 159.ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • V. S. Melezhik
    • 1
  1. 1.Joint Institute for Nuclear ResearchDubna, MoscowUSSR

Personalised recommendations