Por favor, use este identificador para citar o enlazar este ítem:http://uvadoc.uva.es/handle/10324/40873
Título
Second harmonic Hamiltonian: Algebraic and Schrödinger approaches
Año del Documento
2020
Documento Fuente
Phys. Lett. A 384 (2020) 126091
Résumé
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.
ISSN
0375-9601
Revisión por pares
SI
Idioma
eng
Tipo de versión
info:eu-repo/semantics/draft
Derechos
openAccess
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