Time Evolution of a Wave Function

In Part A of this tutorial, an electron is in a one-dimensional infinite square well of width L.  This section contains four questions and two simulations.
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Simulation A.I

Simulation A.I shows the wave function for an electron in the one-dimensional infinite square well. Does the probability density for a given x change with time in this simulation?
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Simulation A.II

Simulation A.II shows the wave function for an electron in the one-dimensional infinite square well. Does the probability density for a given x change with time in this simulation?  Reconcile your observation with the result of Simulation A.I.
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