The aim of this paper is to explore the effect of coupling between the transverse motion and the longitudinal motion of an electron on the resonant tunneling characteristics in a multibarrier heterostructure.A method developed in a previous paper is extended to derive the related formula for the transmission coefficients depending on both the transverse wave number and the longitudinal kinetic energy of an incident electron.A static field is introduced to discuss the influence of the bias voltage on the transmission coefficients

and also to investigate the effect of the coupling between the components of the motion of an electron in the directions of parallel and perpendicular to the interface.A numerical calculation is carried out for the rectangular and parabolic-barrier heterostructures consisting of CdSe/Zn

1-x

Cd

x

Se.In the case of without a bias voltage

it is found that the coupling effect not only leads to a move of the resonant peaks toward the low-energy region

but also causes the broadening of the resonant peaks and the reduction of the peak-to-valley ratio in the transmission spectrum.The influence of the transverse motion of an electron on the higher-lying resonant states for the resonant tunneling is more remarkable than that on the lower-lying resonant states.When the bias voltage is non-zero

a same conclusion is obtained:the resonant peaks also move towards the high-energy region.In addition

when the transverse wave number is constant

the resonant peaks also move towards the low-energy region.Furthermore

the resonant peaks in the lower region will disappear as the bias voltage increases.It is shown that the coupling between components of the motion of the electron in direction parallel and perpendicular to the interface is significant for the resonant-tunneling.