Algebraic approaches and their connection with phase space methods: Applications to spectroscopy

Lemus, Renato

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https://hdl.handle.net/2142/100476 Copy

Description

Title

Algebraic approaches and their connection with phase space methods: Applications to spectroscopy

Author(s)

Lemus, Renato

Issue Date

2018-06-18

Keyword(s)

Mini-symposium: New Ways of Understanding Molecular Spectra

Abstract

First the salient features of the U(ν + 1) algebraic approach associated to ν equivalent oscillators are presented. Then we introduce the 1D case through the connection of the U(2) algebra with the Morse/Poshl-Teller potentials with the goal ¨ of describing the vibrational degrees of freedom of non linear polyatomic molecules. The coordinates and momenta are then identified and generalized to any potential, providing the possibility to solve the 1D Schrodinger equation for general ¨ potentials by purely algebraic means using the concept of transformation brackets. A new procedure to calculate of FranckCondon factors is presented. Because of their importance in linear molecules the U(3) model is introduced, emphasizing its connection with configuration space. It is shown the application of the U(2) × U(3) × U(2) algebraic approach to describe the Raman spectroscopy of the CO2 molecule. The U(3) model is applied to consider general potentials to describe linear-to-bend transition in triatomic molecules. Finally the U(4) model is introduced to describe 3D systems for general potentials. The Hydrogen atom as well as the 3D Morse systems are analyzed by purely algebraic means as a benchmark to show how to apply the algebraic method for potentials with spectroscopic interest.

Publisher

International Symposium on Molecular Spectroscopy

Type of Resource

text

Language

eng

Permalink

http://hdl.handle.net/2142/100476

DOI

10.15278/isms.2018.MH01

Copyright and License Information

Copyright 2018 Renato Lemus

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