# 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

#### 3 Citations

On some polynomial potentials in d-dimensions

- Mathematics
- 2013

The d-dimensional Schrodinger's equation is analyzed with regard to the existence of exact solutions for polynomial potentials. Under certain conditions on the interaction parameters, we show that… Expand

Development of the perturbation theory using polynomial solutions

- Physics
- 2019

The number of quantum systems for which the stationary Schrodinger equation is exactly solvable is very limited. These systems constitute the basic elements of the quantum theory of perturbation. The… Expand

Exact and approximate solutions to Schrödinger’s equation with decatic potentials

- Mathematics, Physics
- 2013

The one-dimensional Schrödinger’s equation is analysed with regard to the existence of exact solutions for decatic polynomial potentials. Under certain conditions on the potential’s parameters, we… Expand

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