  We study the bremsstrahlung radiation of a tunneling charged particle in a
time-dependent picture. In particular, we treat the case of bremsstrahlung
during alpha-decay, which has been suggested as a promissing tool to
investigate the problem of tunneling times. We show deviations of the numerical
results from the semiclassical estimates. A standard assumption of a preformed
particle inside the well leads to sharp high-frequency lines in the
bremsstrahlung emission. These lines correspond to "quantum beats" of the
internal part of the wavefunction during tunneling arising from the
interference of the neighboring resonances in the well.
