2024-03-28T18:17:06Zhttps://uvadoc.uva.es/oai/requestoai:uvadoc.uva.es:10324/408732021-06-24T07:22:49Zcom_10324_22154com_10324_954com_10324_894col_10324_22155
00925njm 22002777a 4500
dc
Mohamadian, T.
author
Panahi, H.
author
Negro Vadillo, Francisco Javier
author
2020
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.
Phys. Lett. A 384 (2020) 126091
0375-9601
http://uvadoc.uva.es/handle/10324/40873
10.1016/j.physleta.2019.126091
126091
3
Physics Letters A
384
Second harmonic Hamiltonian: Algebraic and Schrödinger approaches