Variational coupling between q-number and c-number dynamics
Creators
- 1. Rio de Janeiro Univ. (Brazil). Inst. de Fisica
- 2. Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro
Description
The time dependent quantum variational principle for Hamiltonian operators, which contain real parameters and its time derivatives is generated. The consequent variational system is formed by a Schroedinger equation coupled to Lagrangian equations, where the Lagrangian is the spectation mean value of the parametrized Hamiltonian operator. This dynamics describes the interaction between a q-number sub-dynamics and a c-number one. In the zero order W.K.B. approximation, the variational system is reduced to a Hamilton-Jacobi like equation, coupled to a family of Lagrangian equations. The formal structure of the parametrized variational principle postulated in this paper, may be convenient as a starting point for the formal treatment of generalized semi-classical models. (Author)
Abstract (Portuguese)
Generaliza-se o principio variacional quantico, dependente do tempo, para o caso de operadores Hamiltonianos contendo parametros reais e suas derivadas temporais. O sistema variacional obtido e constituido de uma equacao de Schroendiger acoplada a um sistema de equacoes de Lagrange, onde a Lagrangeana e o valor medio do operador Hamiltoniano parametrizado. A dinamica consequente do principio variacional, descreve a interacao entre uma sub-dinamica q-number com uma subdinamica c-number. Na aproximacao W.K.B. de ordem (h/2π) sup(o), o sistema variacional reduz-se a uma equacao do tipo Hamilton-Jacobi, acoplada a uma familia de equacoes de Lagrange. As caracteristicas formais do sistema variacional obtido sao apropriadas para a descricao de interacoes q-number-c-number, adiabaticas e nao adiabaticas, dependentes do tempo. (Autor)Additional details
Publishing Information
- Journal Title
- Rev. Bras. Fis.
- Journal Volume
- 14
- Journal Issue
- 4
- Series
- Rev. Bras. Fis.
- Journal Page Range
- 477-487
- ISSN
- 0374-4922
- CODEN
- RBFSA
INIS
- Country of Publication
- Brazil
- Country of Input or Organization
- Brazil
- INIS RN
- 17004205
- Subject category
- S71: CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS;
- Descriptors DEI
- DYNAMICS; HAMILTONIANS; LAGRANGIAN FUNCTION; QUANTIZATION; SCHROEDINGER EQUATION; SEMICLASSICAL APPROXIMATION; TIME DEPENDENCE; VARIATIONAL METHODS
- Descriptors DEC
- DIFFERENTIAL EQUATIONS; EQUATIONS; FUNCTIONS; MATHEMATICAL OPERATORS; MECHANICS; PARTIAL DIFFERENTIAL EQUATIONS; QUANTUM OPERATORS; WAVE EQUATIONS