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Schwinger's Variational Principle
The Schwinger's quantum action principle is a variational method, variational approach to quantum mechanics and quantum field theory. This theory was introduced by Julian Schwinger in a series of articles starting 1950. Approach In Schwinger's approach, the Action (physics), action principle is targeted towards quantum mechanics. The action becomes a quantum action, i.e. an operator, S . Although it is superficially different from the path integral formulation where the action is a classical function, the modern formulation of the two formalisms are identical. Suppose we have two states defined by the values of a complete set of commuting operators at two times. Let the early and late states be , A \rang and , B \rang, respectively. Suppose that there is a parameter in the Lagrangian which can be varied, usually a source for a field. The main equation of Schwinger's quantum action principle is: : \delta \langle B, A\rangle = i \langle B, \delta S , A\rangle,\ where the d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schwinger Variational Principle
Schwinger variational principle is a variational principle which expresses the scattering T-matrix method, T-matrix as a Functional (mathematics), functional depending on two unknown wave functions. The functional attains stationary value equal to actual scattering T-matrix. The functional is stationary if and only if the two functions satisfy the Lippmann-Schwinger equation. The development of the variational formulation of the scattering theory can be traced to works of L. Hultén and J. Schwinger in 1940s.R.G. Newton, Scattering Theory of Waves and Particles Linear form of the functional The T-matrix expressed in the form of stationary value of the functional reads : \langle\phi', T(E), \phi\rangle = T[\psi',\psi] \equiv \langle\psi', V, \phi\rangle + \langle\phi', V, \psi\rangle - \langle\psi', V-VG_0^(E)V, \psi\rangle , where \phi and \phi' are the initial and the final states respectively, V is the interaction potential and G_0^(E) is the retarded Green's operator for collis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |