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Painlevé test and energy level motion

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Abstract

From the eigenvalue Hλ|ψn(λ)〉=En(λ) |ψn(λ)〉, where Hλ≡H0+λV, one can derive an autonomous system of first-order differential equations for the eigenvaluesE n(λ) and the matrix elements Vmn(λ), where λ is the independent variable. We perform a Painlevé test for this system and discuss the connection with integrability. It turns out that the equations of motion do not pass the Painlevé test, but a weaker form. The first integrals are polynomials and can be related to the Kowalewski exponents.

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Authors and Affiliations

  1. Department of Applied Mathematics and Nonlinear Studies, Rand Afrikaans University, 2000, Johannesburg, South Africa

    W. -H. Steeb, S. J. M. Brits & N. Euler

Authors
  1. W. -H. Steeb
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  2. S. J. M. Brits
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  3. N. Euler
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Steeb, W.H., Brits, S.J.M. & Euler, N. Painlevé test and energy level motion. Int J Theor Phys 29, 637–642 (1990). https://doi.org/10.1007/BF00672037

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  • DOI: https://doi.org/10.1007/BF00672037

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