2010The Journal of Chemical PhysicsRequires access

Tunneling dynamics and spawning with adaptive semiclassical wave packets

Vasile Gradinaru, George A. Hagedorn, Alain Joye

Open publisher page 17 citations

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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What this paper is about

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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OpenAlex reports 17 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available 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.

Key concepts: Semiclassical physics, Wave packet, Ansatz, Benchmark (surveying), Quantum tunnelling, Network packet, Physics, Quantum mechanics

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