Supersymmetric infinite wells and coherent states

International Conference on 'Quantum Control, Exact or Perturbative, Linear or Nonlinear' to celebrate 50 years of the scientific career of Professor Bogdan Mielnik

Fiset, M.-A.^1 ; Hussin, V.^2,3

Department of Physics, McGill University, Montréal, QC

H3A 2T8, Canada^1

Département de Mathématiques et de Statistique, Université de Montréal, C. P. 6128, Succ. Centre-ville, Montréal

Qc

H3C 3J7, Canada^2

Centre de Recherches Mathématiques, Université de Montréal, C. P. 6128, Succ. Centre-ville, Montréal

Qc

H3C 3J7, Canada^3

关键词: Coherent state;    Gaussian state;    Gaussians;    Heisenberg uncertainty relation;    Localised;    Quantum modeling;    Short periods;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/624/1/012016/pdf
DOI  :  10.1088/1742-6596/624/1/012016

来源: IOP

【 摘 要 】

Gaussian Klauder coherent states are discussed in the context of the infinite well quantum model, otherwise known as the particle in a box. A supersymmetric partner system is also presented, as well as a construction of coherent states in this new system. We show that these states can be chosen, in both systems to have many properties usually expected for coherent states. In particular, they yield highly localised wave packets for a short period of time, which evolve in a quasi-classical manner and which saturate approximately Heisenberg uncertainty relation. These studies are elaborated in one- and two-dimensional contexts. Finally, some relations are established between the Gaussian states being mostly used here and the generalised coherent states, which are more standardly found in the literature.