Simulações de Monte Carlo quântico: técnica variacional e integral de caminho

• Ano de defesa: 2009
• Autor(a) principal: Anna Lucia Silveira Rodrigues de Oliveira
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Minas Gerais; UFMG
• Palavras-chave em Português: Oscilador harmônico; Átomo de hidrogênio; Molécula de hidrogênio ionizada; Função de onda; Integral de caminho; Método de Monte Carlo quântico; Método estocástico; Simulação computacional; Sistema atômico; Processo estocástico; Sistema molecular; Física
• Link de acesso: http://hdl.handle.net/1843/ESCZ-7YSG93

The Monte Carlo method is one of a series called stochastic methods which are characterized by employment of a random sequence of events for evaluating integrals numerically. The set of techniques that apply Monte Carlo method to calculate quantum properties of atomic and molecular systems is generally known as Quantum Monte Carlo In this work we performed quantum Monte Carlo simulations by applying two techniques: The variational method and the path integral approach. Based on the variational principle of quantum mechanics, the variational method allows us to obtain good estimates of energy and wave function of the ground state of a system. The path integral Monte Carlo method is based on the formalism of Feynman path integrals. With this technique, it is possible to make estimates of thermodynamic properties of the system at non-zero temperatures. Some of the systems that we studied using these techniques were the harmonic oscillator, the hydrogen atom and the hydrogen molecule ion. In addition, we obtained the curves of vibrational energy versus temperature of two diatomic molecules, H2 eO2, modeled by the Lennard-Jones potential.