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IEEE/ASME International Conference on Mechatronic and Embedded Systems and Applications

Solving for Quantum Controls

Katherine A. Kime

Published Jan 1, 2011• 0 citations
Publisher

Abstract

We study the use of a time-dependent potential barrier to control quantum wave packets, in a discretization of the Schroedinger equation. We consider computational issues in solving for a control which steers an initial single peak wave packet to a terminal double peak wave packet.
DOI
10.1115/detc2011-48029

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2重障壁ポテンシャルに障壁よりも低いエネルギーをもつ台形波束を入射して共鳴トンネル現象が観測されるか調べた。時間を含む1次元シュレディンガー方程式を数値的に解き,パソコン画面上で波束の運動を観察した。共鳴は,2重障壁の間に波束が長時間にわたって多量にたまることによって識別できた。また,波束をフーリエ変換して得た波数分布から透過波と反射波の割合をみることによって,波束が2重障壁をトンネル透過する程度が判別できた。2重障壁の固有の量子エネルギー準位に対応して台形波束が2重障壁を共鳴的にトンネル透過することが,いろいろな条件の場合について,鮮明に観測された。その結果,2重障壁は特定のエネルギーを持つ波束すなわち粒子のみを選択的に透過させる優れたフィルターの役割をすることがわかった。|A resonance tunnel effect was investigated by leading a wave-packet of trapezoid shape into double potential barriers. The time-dependent Schrödinger equation was numerically solved, and the motion of a wave packet was observed on the screen of a personal computer. The state that a wave packet is resonant with double potential barriers showed a distinct phenomenon that a large part of a wave packet is stored between two barriers for a long time. Tunneling of a wave packet was clearly recognized by comparing an amount of the transmitted wave with that of the reflected one in the distribution of wave vectors that was obtained by the Fourier transformation of a wave packet. A resonance tunnel effect was demonstrated for various kinds of double potential barriers. It was showed that a couple of double potential barriers functions as an excellent filter that allows particles with specified energies to pass through.