Eigenvalue bounds for polynomial central potentials in d dimensions

@article{Katatbeh2007EigenvalueBF,
  title={Eigenvalue bounds for polynomial central potentials in d dimensions},
  author={Q. Katatbeh and R. Hall and N. Saad},
  journal={Journal of Physics A},
  year={2007},
  volume={40},
  pages={13431-13442}
}
If a single particle obeys non-relativistic QM in Rd and has the Hamiltonian H = −Δ + f(r), where , then the eigenvalues E = E(d)nl(λ) are given approximately by the semi-classical expression . It is proved that this formula yields a lower bound if Pi = P(d)nl(q1), an upper bound if Pi = P(d)nl(qk) and a general approximation formula if Pi = P(d)nl(qi). For the quantum anharmonic oscillator f(r) = r2 + λr2m, m = 2, 3, ... in d dimension, for example, E = E(d)nl(λ) is determined by the algebraic… Expand
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