2024-03-29T12:13:11Zhttps://uvadoc.uva.es/oai/requestoai:uvadoc.uva.es:10324/408732021-06-24T07:22:49Zcom_10324_22154com_10324_954com_10324_894col_10324_22155
Second harmonic Hamiltonian: Algebraic and Schrödinger approaches
Mohamadian, T.
Panahi, H.
Negro Vadillo, Francisco Javier
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.
2020-05-16T11:29:01Z
2020-05-16T11:29:01Z
2020
info:eu-repo/semantics/article
info:eu-repo/semantics/draft
https://doi.org/10.1016/j.physleta.2019.126091
Phys. Lett. A 384 (2020) 126091
0375-9601
http://uvadoc.uva.es/handle/10324/40873
126091
3
Physics Letters A
384
eng
info:eu-repo/semantics/openAccess
application/pdf