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I am studying numerical methods for solving the time-dependent Schrödinger equation and simulated the tunnelling of a gaussian wavepacket through a potential barrier. During the simulation I keep track of the expectation value of position of the part of the wavefunction which travels through the barrier. Surprisingly, the wavepacket that tunnels through the barrier propagates slightly further than a wavepacket in a different simulation with no potential barrier. What is the reason for "gaining speed" in the case of the potential barrier compared to the free case?

I was thinking about the potential barrier as some sort of filter, which absorbs the low momentum modes and therefore the transmitted wavefunction is a bit faster, than in the case without a potential barrier.

To visualize the problem stated I attached this photo.

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  • $\begingroup$ "I keep track of the expectation value of....", do you mean the expectation value of position? $\endgroup$ – K_inverse May 29 at 9:22
  • $\begingroup$ Sorry for being unprecise here. Yes, I mean the expectation value of position. $\endgroup$ – Schnarco May 29 at 9:42

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