Abstract
The long-time behaviour of an initially localized quantum state is shown to decay as t –3/2 for any potential well and any potential barrier. An example using a delta barrier is also calculated fully. The result is general yet the proof uses a simple method that is clear and accessible to a wide audience. The effect of bound states on the long-time behaviour is also considered. When there are bound states the long-time behaviour is different.PACS Nos.: 03.65.–w, 03.65.Xp
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