Time-dependent functional Schrodinger picture approach to many-particle systems

A time-dependent many-body theory for many-particle systems is formulated using the functional Schrodinger picture. Taking a Gaussian trial wave functional and using the variational principle, the equations of motion are obtained. The equations of motion are solved in the small oscillation regime to yield the generalized RPA results. The electron-hole excitation, the collective plasma oscillation for the paramagnetic state, the Stoner excitation and the spin wave for the ferromagnetic state are derived and discussed. As a further test on the versatility of the present method, the formalism is applied to the bound states of the exciton problem and shown to yield the governing equation in a straightforward manner.