• 教学讨论 •

### 一维双方势垒量子隧穿的研究及其数值模拟

1. 西安工业大学 基础学院物理系，陕西 西安 710021
• 收稿日期:2021-06-13 修回日期:2021-08-20 出版日期:2022-01-20 发布日期:2022-01-11
• 作者简介:李海凤( 1986—) ，内蒙古呼伦贝尔市人，西安工业大学基础学院物理系，讲师，博士，主要从事理论物理研究和教学工作.
• 基金资助:
国家自然科学基金( 21703166，11647049) ; 陕西省高校科协人才托举项目( 20180605) 资助

### Study and numerical simulation of quantum tunneling for one-dimensional double square potential barriers

LI Hai-feng，WANG Xin-mao

1. School of Science，Xi’an Technological University，Xi’an，Shaanxi 710021，China
• Received:2021-06-13 Revised:2021-08-20 Online:2022-01-20 Published:2022-01-11

Abstract:

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 / U₀) . Finally，the results show

that the transmis-sion 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 / U₀. When the spacing of the double potential barriers is larger，the oscillation

period of the transmission coeffi- cient is larger，while the oscillation amplitude becomes

smaller，with the increase of E / U₀. Therefore，the particle is easier to realize resonant

tunneling in this case.