Anharmonicity deformation and curvature in supersymmetric potentials

Bijan Kumar Bagchi, K. Samanta

Allagbé E. Dossou, F. A. Dossa

Victor Atanasov, Rossen Dandoloff

Dennis Bonatsos A, C. Daskaloyannis

Dongsu Bak A, S P Kim, S K Kim +2 more

We have studied the underlying algebraic structure of the anharmonic oscillator by using the variational perturbation theory. To the first order of the variational perturbation, the Hamiltonian is found to be factorized into a supersymmetric form in terms of the annihilation and creation operators, which satisfy a q-deformed algebra. This algebraic structure is used to construct all the eigenstates of the Hamiltonian.

V. Chithiika Ruby, M. Lakshmanan

Abstract The two-dimensional Mathews–Lakshmanan oscillator, which can be viewed as the planar representation of a harmonic oscillator on a space of constant curvature expressed in Euclidean coordinates, is characterized by a non-standard Hamiltonian. And it can be equivalently interpreted as a position-dependent mass system. Its quantum counterpart is exactly solvable. In this paper, we factorize the associated Hamiltonian and construct the corresponding deformed ladder operators, which do annihilation and creation operations on the eigenstates of the system and also relate them with the eigenstates of the superpartners. We analyze the shape-invariance property of the supersymmetric partner potentials and identify the underlying algebra that leads to the construction of the nonlinear coherent states for the system.