RT info:eu-repo/semantics/article
T1 Second harmonic Hamiltonian: Algebraic and Schrödinger approaches
A1 Mohamadian, T.
A1 Panahi, H.
A1 Negro Vadillo, Francisco Javier
AB We study in detail the behavior of the energy spectrum for the second harmonic generation (SHG) and a family of corresponding quasi-exactly solvable Schrödinger potentials labeled by a real parameter b. The eigenvalues of this system are obtained by the polynomial deformation of the Lie algebra representation space. We have found the bi-confluent Heun equation (BHE) corresponding to this system in a differential realization approach, by making use of the symmetries. By means of a b-transformation from this second-order equation to a Schrödinger one, we have found a family of quasi-exactly solvable potentials. For each invariant n-dimensional subspace of the second harmonic generation, there are either n potentials, each with one known solution, or one potential with n-known solutions. Well-known potentials like a sextic oscillator or that of a quantum dot appear among them.
SN 0375-9601
YR 2020
FD 2020
LK http://uvadoc.uva.es/handle/10324/40873
UL http://uvadoc.uva.es/handle/10324/40873
LA eng
NO Phys. Lett. A 384 (2020) 126091
DS UVaDOC
RD 26-abr-2024