Abstract
A semiclassical method for solving the quantum Liouville equation in one-dimensional phase-space is described. The development is based on constructing a Gaussian density matrix and is applicable to systems in pure and in mixed states having nonlinear interaction potentials. The density matrix is constructed using a set of dynamic variables whose expectation values are considered to be relevant for the dynamics. The self-consistent equations of motion are then derived for these expectations from the quantum Liouville equation using a projection scheme. The solution of these self-consistent equations provides the time evolution of the density matrix. The present method can yield, in principle, exact values for these expectations for all times. A model calculation is carried out to describe the vibrational motion of an arbitrary diatomic molecule on an anharmonic potential surface. However, the potentiality of this method lies in describing the time evolution of systems in mixed states and hence in describing the dynamics of molecular processes in condensed phases.
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Haque, A., George, T.F. (1988). Semiclassical Molecular Dynamics of Wavepackets in One-Dimensional Phase Space. In: Arponen, J.S., Bishop, R.F., Manninen, M. (eds) Condensed Matter Theories. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0971-0_10
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DOI: https://doi.org/10.1007/978-1-4613-0971-0_10
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