Hamiltonian hierarchy and the Hulthén potential

Abstract

We deal with the Hamiltonian hierarchy problem of the supersymmetry quantum mechanics for the Hulthen potential and find that the associated "supersymmetric partners" belong to the Eckart class of potentials. The partner potentials, on the one hand, simulate the effect of the centrifugal barrier fairly accurately at least for few lower partial waves and, on the other hand, provide a natural basis for writing expressions for higher partial wave Jost functions. We present specific results for the p and d waves and examine their Coulomb limits.which has a ground state ()pI) ', EI) ') can be factorized as

Hamiltonian hierarchy and the Hulthén potential

“…The supersymmetric formalism has already been used to study some aspects of the Hulthén potential [15,17]. Here the exact analytical solution for this potential is re-obtained for ℓ = 0 state in the light of the works described in Refs.…”

“…Here the exact analytical solution for this potential is re-obtained for ℓ = 0 state in the light of the works described in Refs. [15][16][17]20] to show the consistency of the method and see how partners of the Hulthén potential simulate the effect of the centrifugal barrier, which makes clear the physics behind partner Hamiltonians in connection with the states having ℓ = 0 angular momenta. In the approach followed here the first step taken is to look for an effective potential similar to the original Hulthén potential.…”

Supersymmetry, Variational Method and Hulthén Potential

“…We start from V ef f given by (14) whose eigenfunctions are given by (8) and (19). For the state 2p we use the first member of the superfamily (l = 1) as our trial wave function, changing δ by the variational parameter µ, i.e.,…”

Localization of a nonlocal interaction

“…Here ϕ H (k, r) and f H (k, r) stand for the regular and irregular solutions of pure Hulthén potential [26,27] and…”

“…(2), (5), (10), (12), (21), (25), (27), (29), (38), (39), and (48) the same for the irregular boundary condition is obtained as…”