Schrödinger spectrum generated by the Cornell potential

Abstract

Abstract:The eigenvalues E d n (a, c) of the d-dimensional Schrödinger equation with the Cornell potential V(r) = −a/r + c r, a, c > are analyzed by means of the envelope method and the asymptotic iteration method (AIM). Scaling arguments show that it is su cient to know E( , 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 e ort.

Heavy-Quarkonium Potential from Lattice Gluon Propagator

“…We must consider that, in this comparison, our parameters are close to but not identical to the ones used in Ref [13],. which might explain the slightly worse agreement than in the comparison with[29].…”

“…We therefore add a linear term to V LGP , obtaining the V LGP+L potential in Eq. (29). We solve the associated Schrödinger equation numerically and compare our results with the spin-averaged spectrum.…”

WKB Energy Expression for the Radial Schrödinger Equation with a Generalized Pseudoharmonic Potential

“…Some of these potentials are exactly solvable while the non-exactly solvable potentials can be approximated by using a numerical approach and appropriate analytical methods. Some methods that are routinely used to estimate the bound states solutions of the SE are the Asymptotic iterative method [1][2][3][4], Nikiforov-Uvarov method [5][6][7][8][9], supersymmetric quantum mechanics approach [10,11] analytical exact iterative method [12], / expansion approach [13], Artificial neural network scheme [14], the WKB approximation method [15][16][17][18][19][20][21][22] and so on.…”

Remarks on the treatments of nonsolvable potentials

“…The Schrödinger equation with the Cornell potential, V (r) = − a r + br , also known as the Coulomb plus linear potential, has received a great deal of attention [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] as an important nonrelativistic model in both particle physics, or more precisely in the context of meson spectroscopy, where it is used to describe systems of quark and antiquark bound states, and in atomic and molecular physics, where it represents a radial Stark effect in hydrogen. Aside from the physical relevance, the solutions of the Schrödinger equation for the Coulomb plus linear potential have been rigorously investigated with a large number of techniques [5,8,[10][11][12][13][14][15][16][17][18][19] due to its nontrivial mathematical properties. In addition, this potential has an advantage that leads naturally to two choices of parent Hamiltonian in perturbative treatments, one based on the Coulomb part and the other on the linear term, which can be usefully compared.…”