Supersymmetry, Variational Method and Hulthén Potential

Abstract

The formalism of Supersymmetric Quantum Mechanics provides us the eigenfunctions to be used in the variational method to obtain the eigenvalues for the Hulthén Potential.

Application of the Nikiforov-Uvarov Method in Quantum Mechanics

“…The Hulthen potential has been used in several branches of physics such as nuclear and particle, atomic, molecular and chemical physics (Durand & Durand, 1981;Xu et al, 2006;Bitensky et al, 1997;Jia et al, 2000;Olson & Micha, 1978). Moreover, its discrete and continuum states have been studied by a variety of techniques such as the supersymmetry and shape invariance property (Varshni, 1990;Filho & Ricotta, 1995;Qian et al, 2002). The solution of the SE for a particle in the Hulthen potential can not be obtained exactly for the case of ℓ = 0 whereas we have an exact solution for the case of ℓ = 0, namely s-wave solution (Flügge, 1971).…”

Hamiltonian hierarchy and the Hulthén potential

“…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.…”

Estudo da equação de Fokker-Planck para os potenciais de Hulthén e de Morse generalizado via supersimetria

“…Os potenciais de Hulthén [2] e de Morse generalizado [1] são bastante utilizados no contexto biofísico, o potencial de Hulthén, por exemplo,é utilizado para descrever interações atômicas com aplicações em física nuclear, em física do estado sólido e em fisico-química e o potencial de Morse generalizado, descreve moléculas diatômicas e modelos físicos para o DNA [3].…”