COMPARATIVE STUDY OF SEMICLASSICAL APPROACHES TO QUANTUM DYNAMICS
Quantum states can be described equivalently by density matrices, Wigner functions, or quantum tomograms. We analyze the accuracy and performance of three related semi-classical approaches to quantum dynamics, in particular with respect to their numerical implementation. As test cases, we consider the time evolution of Gaussian wave packets in different one-dimensional geometries, whereby tunneling, resonance, and anharmonicity effects are taken into account. The results and methods are benchmarked against an exact quantum mechanical treatment of the system, which is based on a highly efficient Chebyshev expansion technique of the time evolution operator.
wigner function chebyshev expansion time evolution of quantum systems quantum tomography semiclassical approximation