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 behavior becomes predominant at short distances and short times, as we should expect. 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 modified time-energy uncertainty relation in the polymer framework is briefly discussed.

• Received 12 June 2014

DOI:https://doi.org/10.1103/PhysRevD.90.125027