Linearized coherent states for Hamiltonian systems with two equidistant ladder spectra

8th International Symposium on Quantum Theory and Symmetries

Bermudez, D.^1,2 ; Contreras-Astorga, A.^1 ; Fernández C, D.J.^1

Departamento de Física, Cinvestav, A.P. 14-740, 07000 México D.F., Mexico^1

Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel^2

关键词: Coherent state;    Finite subspaces;    Hamiltonian systems;    Harmonic oscillators;    Supersymmetric quantum mechanics;    Third order;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/512/1/012018/pdf
DOI  :  10.1088/1742-6596/512/1/012018

来源: IOP

【 摘 要 】

A simple way to construct exactly solvable Hamiltonians whose spectra contain two equidistant ladders, one finite and another infinite, appears when applying supersymmetric quantum mechanics to the harmonic oscillator. Some of those supersymmetric partners have third order differential ladder operators, although the order of the transformation is higher than one. In this work the linearized coherent states for these specific Hamiltonians are studied. To each SUSY partner Hamiltonian corresponds two families of linearized coherent states: one inside the subspace associated with the isospectral part of the spectrum and another one in the finite subspace generated by the states inserted through the SUSY technique.