An algebraic dvr approach to describe the stark effect

Bermúdez Montaña, Marisol

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https://hdl.handle.net/2142/107598 Copy

Description

Title

An algebraic dvr approach to describe the stark effect

Author(s)

Bermúdez Montaña, Marisol

Contributor(s)

• E., Orgaz Baque
• Lemus, Renato
• Rodríguez Arcos, Marisol

Issue Date

2020-06-23

Keyword(s)

Theory and Computation

Abstract

An algebraic approach based on the $U(4)$ algebra is proposed to describe 3D systems for effective potentials. Our approach is based on the addition of a scalar boson to the 3D harmonic oscillator space keeping the constraint of a total number of bosons N constant, in similar form as in the vibron model. However instead of dealing directly with the dynamical symmetries we proceed to identify the coordinates and momenta in the algebraic space. This allows the kets associated with the different subgroup chains to be linked to energy, coordinate and momentum representations. This identification provides powerful tools to obtain the matrix representation of 3D Hamiltonians in a simple form through the use of the transformation brackets connecting the different bases. The exact energy and wave functions are obtained in the large $N$ limit. Because the relevance of the Coulomb interaction we consider as an example of our approach the analysis of the non relativistic Hydrogen atom as a first step to establish the ground to deal with multi-electron molecular systems.

Publisher

International Symposium on Molecular Spectroscopy

Type of Resource

Text

Language

eng

Permalink

http://hdl.handle.net/2142/107598

Copyright and License Information

Copyright 2020 is held by the Author(s)

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