Overlaps of deformed and non-deformed harmonic oscillator basis states

• Published in: Physics letters. A Vol. 384; no. 7; p. 126162
• Main Authors: Kekejian, David, Draayer, Jerry P., Dytrych, Tomáš, Launey, Kristina D.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 09-03-2020
• Subjects: Deformed overlaps; Harmonic oscillator; Interbasis expansion; Interbasis expansion; Deformed overlaps; Harmonic oscillator
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2019.126162

•Analytic results were derived for the first time between deformed and non-deformed harmonic oscillator basis states.•The overlaps are independent of the harmonic oscillator frequency in a given space, deformed or non-deformed.•Useful for studying coupled oscillators, nuclear shell model, coherent state theory, deformed effective field theory and damped oscillators.
A systematic approach for expanding non-deformed harmonic oscillator basis states in terms of deformed ones, and vice versa, is presented. The objective is to provide analytical results for calculating these overlaps (transformation brackets) between deformed and non-deformed basis states in spherical, cylindrical, and Cartesian coordinates. These overlaps can be used for reducing the complexity of different research problems that employ three-dimensional harmonic oscillator basis states, for example as used in coherent state theory and the nuclear shell-model, especially within the context of ab initio symmetry-adapted no-core shell model.