一维双方势垒量子隧穿的研究及其数值模拟

Study and numerical simulation of quantum tunneling forone-dimensional double square potential barriers

量子隧穿效应在实际技术中具有重要应用,本文首先展示了如何求解一维任意边界非对称以及对称双方势垒的透射系数,然后研究了对称双方势垒透射系数对垒宽、垒间距以及微观粒子入射能量与垒高比值(E/U 0)的变化依赖关系.最终得出以下结论,随着双方势垒垒宽的增加,透射系数从最大值1衰减至最小值0.随着垒间距的增加,透射系数呈现周期振荡,本文首次推导得出透射系数最大时对应的垒间距解析表达式,并给出振荡的周期,进一步证明得到它等于微观粒子的德布罗意波长.当垒宽越小时,随着E/U 0的增大,透射系数更容易达到1,并且保持不变,当垒间距越大时,随着E/U 0的增大,透射系数振荡周期变大,而振幅变小,粒子更容易实现共振隧穿.

Quantum tunneling effect has important applications in practical technology.In this paper,it is shown how to calculate the transmission coefficients of one-dimensional asymmetric and symmetric double square potential barriers with the arbitrary boundary.Then we study the dependence of the transmission coefficients for symmetric double square potential barriers on the barrier width,the spacing between the two barriers and the ratio of the incident energy of microscopic particles to barrier height(E/U 0).Finally,the results show that the transmission coefficient decreases from the maximum value 1 to the minimum value 0 with the increase of the barrier width.Moreover,the transmission coefficient oscillates periodically with the increase of the barrier spacing.The analytical expression of the barrier spacing corresponding to the maximum transmission coefficient is derived,and the period of oscillation is given,which is equal to the de Broglie wave length of the microscopic particle.When the barrier width is smaller,the transmission coefficient is easier to reach and keep the maximum value 1 with the increase of E/U 0.When the spacing of the double potential barriers is larger,the oscillation period of the transmission coefficient is larger,while the oscillation amplitude becomes smaller,with the increase of E/U 0.Therefore,the particle is easier to realize resonant tunneling in this case.