rnWe have used several different methods to solve the one-dimensional, time-dependent Schrodinger equation for a sinusiodally modulated barrier. Analytical solutions are given for the case in which the time-dependent part of the potential has several different forms, but is independent of position. For more general fields, Floquet's theorem is used to write the wavefunction as a summation of components which have different energies as a result of the absorption and emission of modulation quanta. A system of coupled ordinary differential equations is obtained, which is then solved numerically using shooting methods. The examples show a resonance in which the tunneling current is markedly increased. For square barriers, this resonance occurs when the particles absorbing modulation quanta are above the barrier, and the length of the barrier is an integer multiple of one-half the de Broglie wavelength. The existence of the resonance is confirmed by asymptotic solutions for large and small frequencies. Examples suggest that it may be possible to make a microwave power amplifier by illuminating a field emitter array with an amplitude-modulated laser operating near the new resonance. ated much interest and controversy [31. f i s subject has considerable practical significance. For example, the measured tunnel conductance in heterostructures differs from theory by as much as 2 easurements with semiconductor hetorders of magnitude unless the image corrections are modified to allow for the traversal time ill.Furthermore, at high energies it is necessary to include tunneling through the reaction barrier in transition state theory to obtain accurate rate con-