Spectral Sum Rules for Confinement Potentials

  • Frank Steiner
Part of the NATO ASI Series book series (NSSB, volume 144)


Consider the motion of a particle with mass m in the spherically symmetric confinement potential V(r) = grP, g > 0, p > 0. The corresponding radial Schrödinger operator H (with angular momentum ℓ) has only a discrete spectrum, 0 < E0ℓ < E1ℓ, <… Define the energy moments (N ε IN with N > (p+2)/2p)
$$ M_\ell ^{\left( N \right)} \equiv \sum\limits_{m = 0}^\infty {\frac{1}{{E_{n\ell }^N}}} $$
(“Zeta function” of the hermitian operator H evaluated at S = N).


Zeta Function Discrete Spectrum Hermitian Operator Bound State Energy Exact Energy 
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Copyright information

© Plenum Press, New York 1986

Authors and Affiliations

  • Frank Steiner
    • 1
  1. 1.Theoretical Physics DepartmentCERNGeneva 23Switzerland

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