## Time dependent variational approach to semiclassical dynamics

Explicitly time dependent methods for semiclassical dynamics are explored using variational principles. The Dirac--Frenkel--McLachlan variational principle for the time dependent Schrodinger equation and a variational correction procedure for wavefunctions and transition amplitudes are reviewed. These variational methods are shown to be promising tools for the solution of semiclassical problems where the correspondence principle, classical intuition, or experience suggest reasonable trial forms for the time dependent wavefunction. Specific trial functions are discussed for several applications, including the curve crossing problem. The useful semiclassical content of the time-dependent Hartree approximation is discussed. Procedures for the variational propagation of density matrices are alsomore »