  We consider the polymer quantization of the Einstein wormhole throat theory
for an eternal Schwarzschild black hole. We numerically solve the difference
equation describing the quantum evolution of an initially Gaussian,
semi-classical wave packet. As expected from previous work on loop quantum
cosmology, the wave packet remains semi-classical until it nears the classical
singularity at which point it enters a quantum regime in which the fluctuations
become large. The expectation value of the radius reaches a minimum as the wave
packet is reflected from the origin and emerges to form a near Gaussian but
asymmetrical semi-classical state at late times. The value of the minimum
depends in a non-trivial way on the initial mass/energy of the pulse, its width
and the polymerization scale. For wave packets that are sufficiently narrow
near the bounce, the semi-classical bounce radius is obtained. Although the
numerics become difficult to control in this limit, we argue that for pulses of
finite width the bounce persists as the polymerization scale goes to zero,
suggesting that in this model the loop quantum gravity effects mimicked by
polymer quantization do not play a crucial role in the quantum bounce.
