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Spectral Properties of Faddeev Equations in Differential Form

  • S. L. Yakovlev
Part of the Few-Body Systems book series (FEWBODY, volume 10)

Abstract

Faddeev equations in differential form were introduced by Noyes and Fiedeldey in 1968 [1]
$$ ({H_0} - E){\varphi _\alpha } + {V_\alpha }\sum\limits_{\beta = 1}^3 {{\varphi _\beta } = 0,} $$
(1)
and since that time are used extensively for investigating theoretical aspects of the three-body problem as well as for getting numerical solutions of three-body bound-state and scattering state problems. The simple formula
$$ \sum\nolimits_{\beta = 1}^3 {{\varphi _\beta } = \Psi } $$
allows one to obtain the solution to the three-body Schrödinger equation
$$ ({H_0} + \sum\nolimits_{\beta = 1}^3 {{V_\beta } - E} )\Psi = 0 $$
in the case when
$$ \sum\limits_{\beta = 1}^3 {{\varphi _\beta } \ne 0.} $$
(2)
. Such solutions of (1) can be called physical. The proper asymptotic boundary conditions should be added to Eqs. (1) in order to guarantee (2). These conditions were studied by many authors and are well known [2], so that I will not discuss them here.

Keywords

Matrix Operator Total Angular Momentum Schrodinger Equation Faddeev Equation Spurious Solution 
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.

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References

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    H.P. Noyes, H. Fiedeldey: In: Three-particle scattering in quantum mecha-nics, p. 195. New-York-Amsterdam 1968Google Scholar
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Copyright information

© Springer-Verlag/Wien 1999

Authors and Affiliations

  • S. L. Yakovlev
    • 1
  1. 1.Department of Mathematical and Computational PhysicsSt. Petersburg State UniversitySt. Petersburg, PetrodvoretzRussia

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