Tunneling dynamics and spawning with adaptive semi-classical wave-packets

Abstract : Tunneling through a one-dimensional Eckart barrier is investigated using a recently developed propagation scheme based on semiclassical wave packets. This version of the time-dependent discrete variable representation method yields linear equations for the parameters, is fully adaptive, and does not require a frozen ansatz in order to approximate the exact solution of the Schrödinger equation accurately. We rely on an analytical result to derive a new algorithm to spawn a second family of semiclassical wave packets after the tunneling has occurred. Numerical results for a benchmark problem demonstrate the accuracy of the new method.
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Vasile Gradinaru, George Hagedorn, Alain Joye. Tunneling dynamics and spawning with adaptive semi-classical wave-packets. Journal of Chemical Physics, American Institute of Physics, 2010, 132, pp.184108. ⟨hal-00954339⟩

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