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Schrödinger spectrum generated by the Cornell potential

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Hall R. L., Saad N.

Open Physics

2015

vol. 13

issue 1

The eigenvalues Ednl (a, c) of the d-dimensional Schrödinger equation with the Cornell potential V(r) = −a/r + c r, a, c > 0 are analyzed by means of the envelope method and the asymptotic iteration method (AIM). Scaling arguments show that it is suffcient to know E(1, λ), and the envelope method provides analytic bounds for the equivalent complete set of coupling functions λ(E). Meanwhile the easily-implemented AIM procedure yields highly accurate numerical eigenvalues with little computational effort.

Lévy flights and Lévy-Schrödinger semigroups

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Garbaczewski P.

Open Physics

2010

vol. 8

issue 5

699-708

We analyze two different confining mechanisms for Lévy flights in the presence of external potentials. One of them is due to a conservative force in the corresponding Langevin equation. Another is implemented by Lévy-Schrödinger semigroups which induce so-called topological Lévy processes (Lévy flights with locally modified jump rates in the master equation). Given a stationary probability function (pdf) associated with the Langevin-based fractional Fokker-Planck equation, we demonstrate that generically there exists a topological Lévy process with the same invariant pdf and in reverse.

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2 Open Physics

1 2015

1 2010

1 Garbaczewski P.

1 Hall R. L.

1 Saad N.

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Schrödinger spectrum generated by the Cornell potential

Lévy flights and Lévy-Schrödinger semigroups