Abstract
We study non-relativistic propagation of Gaussian wave packets in one-dimensional Eckart potential, a barrier, or a well. In the picture used, the transmitted wave packet results from interference between the copies of the freely propagating state with different spatial shifts (delays), x', induced by the scattering potential. The Uncertainty Principle precludes relating the particle’s final position to the delay experienced in the potential, except in the classical limit. Beyond this limit, even defining an effective range of the delay is shown to be an impracticable task, owing to the oscillatory nature of the corresponding amplitude distribution. Our examples include the classically allowed case, semiclassical tunnelling, delays induced in the presence of a virtual state, and scattering by a low barrier. The properties of the amplitude distribution of the delays, and its pole representation are studied in detail.
Highlights
We study non-relativistic propagation of Gaussian wave packets in one-dimensional Eckart potential, a barrier, or a well
It would be helpful to have a general approach to quantum scattering, setting clear limits on what can and what cannot be asked of a quantum particle
In Section “Apparently “instantaneous” semiclassical tunnelling” we analyse the semiclassical limit of a tunnelling transmission
Summary
We study non-relativistic propagation of Gaussian wave packets in one-dimensional Eckart potential, a barrier, or a well. Large enough for the scattering to be completed, we will compare the positions of the transmitted wave packet with that of a freely propagating one, in order to determine whether the potential delays the particle or makes it, in some sense, go faster.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
