I am currently learning and solving Schrodinger's time independent equation for particles under various 1D-potentials.

Would it be possible to have a mix of a linear potential (of the form $U(x)=Fx$ for example) which is still infinite at every point (of the form $U(x)=\delta(x)$ for example)? The motivation would be that I want the particle to be moving in only one direction without being able to return in the other direction (as if it faces an infinite wall at every point).

I know the question is ill-formulated so please let me know if you need more details.

  • $\begingroup$ $\delta(x)$ is not infinite at every point, and it also doesn't as if you want that. $\endgroup$
    – NDewolf
    Feb 24, 2021 at 8:27
  • $\begingroup$ How is the potential linear and yet infinite at every point? $\endgroup$
    – Triatticus
    Feb 24, 2021 at 8:41
  • $\begingroup$ I think you're looking for a potential of the form $U(x)=Fx$ for $x>0$ and $U(x)=\infty$ for $x\leq 0$. I don't know how to solve it myself but this would correspond to a gravitational potential with a solid wall at $x=0$. $\endgroup$ Feb 24, 2021 at 9:02
  • 2
    $\begingroup$ @AccidentalTaylorExpansion Airy functions are the solutions to such a potential well. $\endgroup$
    – Triatticus
    Feb 24, 2021 at 9:30


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