In this report we investigate the macroscopic quantum tunneling of a Bose
condensate falling under gravity and scattering on a Gaussian barrier that
could model a mirror of far-detuned sheet of light. We analyze the effect of
the inter-atomic interaction and that of a transverse confining potential. We
show that the quantum tunneling can be quasi-periodic and in this way one could
generate coherent Bose condensed atomic pulses. In the second part of the
report, we discuss an effective 1D time-dependent non-polynomial nonlinear
Schrodinger equation (NPSE), which describes cigar-shaped condensates. NPSE is
obtained from the 3D Gross-Pitaevskii equation by using a variational approach.
We find that NPSE gives much more accurate results than all other effective 1D
equations recently proposed.Comment: 9 pages, 5 figures, report for the X International Laser Physics
Workshop, Seminar on Bose-Einstein Condensation of Trapped Atoms, Moscow,
July 3-7, 200
