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Gaussian wavepackets are a popular tool for semiclassical analyses of classically chaotic systems. We demonstrate that they are extremely powerful in the semiquantal analysis of such systems, too, where their dynamics can be recast in an extended potential formulation. We develop Gaussian semiquantal dynamics to provide a phase space formalism and construct a propagator with desirable qualities. We qualitatively evaluate the behaviour of these semiquantal equations, and show that they reproduce the quantal behavior better than the standard Gaussian semiclassical dynamics. We also show that these semiclassical equations arise as truncations to semiquantal dynamics non-self-consistent inh. This enables us to introduce an extended semiclassical dynamics that retains the power of the Hamiltonian phase space formulation. Finally, we show how to obtain approximate eigenvalues and eigenfunctions in this formalism, and demonstrate with an example that this works well even for a classically strongly chaotic Hamiltonian.

The time-dependent variational principle using generalized Gaussian trial functions yields a finite dimensional approximation to the full quantum dynamics and is used in many disciplines. It is shown how these 'semi-quantum' dynamics may be derived via the Ehrenfest theorem and recast as an ex- There has been substantial effort made, over the years, to understand quantum systems using a system of few classical variables. These can be motivated in theh → 0 limit, such as effective potential techniques[1,2] and semi-classical methods like that of WKB, which lead to the Einstein-Brillouin-Keller (EBK) [3] quantization rules for integrable systems. These also include approximations to the Feynman path-integral formulation [4], used to derive the Periodic-Orbit Trace Formula for chaotic systems [5]. This relates the spectrum of the quantum system to a weighted sum over the unstable periodic orbits of the classical system.They can also arise, as in Quantum Chromo Dynamics for example [6], in the limit of large N (number of degrees of freedom), and a classical phase space can be shown to exist in the N = ∞ limit [7]. Further, there are many equivalent mean-field theories that are used in 1