Banca de DEFESA: KARLA PEDROZA OLIVEIRA

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : KARLA PEDROZA OLIVEIRA
DATE: 23/08/2022
TIME: 10:00
LOCAL: Plataforma da conferência WEB - RNP
TITLE:

FUNDAMENTALS OF SPREADING THEORY IN SIMPLETIC QUANTUM MECHANICS

KEY WORDS:

Scattering; Lippmann-Schwinger Equation; Scattering Cross Section; Symplectic Quantum Mechanics; Wigner Function.

PAGES: 99
BIG AREA: Ciências Exatas e da Terra
AREA: Física
SUMMARY:

In this work we present a construction of the scattering theory based on Propagators in Phase Space using the Symplectic Quantum Mechanics (SQM) formalism. Initially, the scattering theory is revisited using Classical Mechanics (CM) and the usual Quantum Mechanics (QM) and cross section expressions based on these theories are developed. Next, the description of Quantum Mechanics in Phase Space as developed by Wigner, Weyl and Moyal is presented to obtain the expression of the cross section in Phase Space in terms of the Wigner function; Symplectic Quantum Mechanics (SQM) is developed and applied to the simple harmonic oscillator as a way of comparing its result with Wigner’s development and having the basic elements of SQM to introduce the propagators in the theory. Introduced the Propagator in Phase Space, using the SQM, we developed the Lippmann-Schwinger Equation (LSE) in Phase Space and obtained solutions for this equation in the one-dimensional and three-dimensional asymptotic cases. In order to test the constructed development, we apply the results to the problem of a particle scattered by a one-dimensional Dirac delta potential and show that the cross section calculated in this new formulation agrees with the one obtained via the usual QM. 

BANKING MEMBERS:
Interno - 664720 - ANTONIO FERREIRA DA SILVA
Interno - 102.263.461-53 - JOSE DAVID MANGUEIRA VIANA - UFBA
Externo à Instituição - ADEMIR EUGENIO DE SANTANA - UnB