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Distribution of Energy Levels in Quantum Systems with Integrable Classical Counterpart. Rigorous Results

  • P. M. Bleher
Conference paper

Abstract

Let E 0E 1E 2 ≤... be the energy levels (eigenvalues) of the Schrödinger operator H = -1/2Δ + U(q) on a closed d-dimensional Riemannian manifold M d . Here
$$- \Delta = - \frac{1}{{\sqrt {g} }}\frac{\partial }{{\partial {q^{i}}}}(\sqrt {g} {g^{{ij}}}\frac{\partial }{{\partial {g^{i}}}})] $$
(1)
is the Laplace-Beltrami operator and to ensure the discreteness of the spectrum of H we assume, in the case of a non-compact M d , that limq→∞ U(q) = ∞. For simplicity we assume also that M d has no boundary. Otherwise it is neccessary to supply H with Dirichlet (or some other) boundary conditions.

Keywords

Spectral Interval Quantum Chaos Schrodinger Operator Revolution Surface Smooth Periodic Function 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • P. M. Bleher
    • 1
  1. 1.Raymond and Beverly Sackler Faculty of Exact Sciences, School of Mathematical SciencesTel Aviv UniversityRamat AvivIsrael

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