Curvature-induced modifications in the algebraic structure of the two-dimensional Mathews–Lakshmanan nonlinear oscillator and the associated coherent states
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.
Physica Scripta•Jul 27, 2026•0 citations