2023/06/13 by Nibaldo-Edmundo Alvarez-Moraga, Alvarez-Moraga, Nibaldo-Edmundo
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Electron Spin Resonance Studies #FOS: Physical sciences #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Spectroscopy and Quantum Chemical Studies
paper · pdf · doi:10.48550/arxiv.2306.07889
openalex publication_date 2023/06/13 · openalex created_date 2023/06/15 · openalex updated_date 2026/07/28
In this article a study was made of the conditions under which a Hamiltonian which is an element of the complex \ h (1) ⊕ h(1) \ \uplus u(2) Lie algebra admits ladder operators which are also elements of this algebra. The algebra eigenstates of the lowering operator constructed in this way are computed and from them both the energy spectrum and the energy eigenstates of this Hamiltonian are generated in the usual way with the help of the corresponding raising operator. Thus, several families of generalized Hamiltonian systems are found, which, under a suitable similarity transformation, reduce to a basic set of systems, among which we find the 1:1, 2:1, 1:2, su(2) and some other non-commensurate and commensurate anisotropic 2D quantum oscillator systems. Explicit expressions for the normalized eigenstates of the Hamiltonian and its associated lowering operator are given, which show the classical structure of two-mode separable and non-separable generalized coherent and squeezed states. Finally, based on all the above results, a proposal for new ladder operators for the p:q coprime commensurate anisotropic quantum oscillator is made, which leads us to a class of Chen SU(2) coherent states.