Algebraic Method for Perturbed Three-Body Systems of Solvable Potential
Feb 12, 2020
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Abstract: (Springer)
In this paper, we try to solve the Schrödinger equation in a quasi-exact solvable method for a three-body problem with a special interaction and by adding an anharmonic perturbation term. We consider the interaction and perturbation theory in the Calogero model by the roots of algebra and rewrite the Hamiltonian in terms of Lie algebra and generators. Indeed, we show that the gauge transformed Hamiltonian has infinite invariant flags with finite-dimension. Finally, we obtain a range of eigenvalues and eigenfunctions corresponding to its corrections by using the algebraic framework of the perturbation theory.- algebra: Lie
- perturbation theory
- Hamiltonian
- Schroedinger equation
- three-body problem
- Calogero model
- perturbation
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