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.

Key words: double square potential barriers, quantum tunneling, resonant tunneling, stationary state Schr?dinger equation