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Nov 13, 2019 at 17:48 comment added Michael Engelhardt Oh yes, all kinds of fun stuff happens in more general cases; and physically relevant potentials usually don't have bounded support anyway.
Nov 13, 2019 at 9:19 history edited Carlo Beenakker CC BY-SA 4.0
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Nov 13, 2019 at 7:38 history edited Carlo Beenakker CC BY-SA 4.0
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Nov 13, 2019 at 7:36 comment added Carlo Beenakker indeed, thanks for correcting me; I was thinking of the more general case where the "line" has a nonzero extension in the transverse direction, then there appear evanscent (decaying) modes even when $V=0$.
Nov 13, 2019 at 0:03 comment added Michael Engelhardt If one assumes, as the OP does, that $V\geq 0$, there are no evanescent waves. Once $V=0$, the solutions to the Schr\"odinger equation are strictly $e^{\pm ipx} $.
Nov 12, 2019 at 21:23 history edited Carlo Beenakker CC BY-SA 4.0
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Nov 12, 2019 at 21:18 history edited Carlo Beenakker CC BY-SA 4.0
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Nov 12, 2019 at 21:13 history answered Carlo Beenakker CC BY-SA 4.0