  We study the quantum dynamics of a suddenly released beam of particles using
a background independent (polymer) quantization scheme. We show that, in the
first order of approximation, the low-energy polymer distribution converges to
the standard quantum-mechanical result in a clear fashion, but also arises an
additional small polymer correction term. We find that the high-energy polymer
behaviour becomes predominant at short distances and short times. Numerical
results are also presented. We find that particles whose wave functions satisfy
the polymer wave equation do not exhibit the diffraction in time phenomena. The
implementation of a lower bound to the possible resolution of times into the
time-energy Heisenberg uncertainty relation is briefly discussed.
