Resonances and wave packets in a potential well followed by a barrier.

Lajos Jánossy

Teruaki Minagawa, Yuko TATSUMI, Miki INOUE

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.

George H. Duffey

Ralph G. Hay, Thomas B. Bahder, John D. Bruno

In order to better understand the trapping and response time of resonant electron wave packets in a resonant tunneling structure, we examined the time-dependent transport of a spherically symmetric Gaussian wave packet through a model double-barrier potential. Within the effective mass picture, the wave packet is projected onto the complete eigenstates of the model potential. The wave packet is initially localized to the left of the barriers and allowed to propagate through the structure. At wave packet energies corresponding to the resonant energies, the probability transmitted to the right of the barriers exhibits a steplike behavior as a function of time. A computation is made of the quantum mechanical delay time, to~tclass, where to is the packet transit time and tclass is the transit time for a classical particle. An increase in this delay time is observed when the packet energy corresponds to the energy of the resonant levels, and a comparison is made to the decay time of a particle in the first resonant state of the well. The delay time increases with increasing barrier area and decreasing packet energy width.

Abdelhamid Albaid

Abstract This paper examines tunnelling through potential well protected by double barriers as well as the motion of a wave packet encountering this type of potential. Various options for the left and right barriers’ penetration factors are taken into consideration. When one of the penetration factors has limiting value of 0.5, the transmission coefficients turns out to be independent of incoming energy of the particle and the width of potential well. When both penetration factors have a limiting value of 0.5, a scenario similar to resonance tunneling is achieved. Furthermore, by doing the wave packet analysis, we found that the width and height of potential barriers have a negligible impact on the probability of finding the particle inside the potential well in the limit of large penetration factors.

Jason Nguyen, Paul Dyke, Alina Blinova +2 more