# Infinite linear potential well?

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.

• $\delta(x)$ is not infinite at every point, and it also doesn't as if you want that. Feb 24 at 8:27
• How is the potential linear and yet infinite at every point? Feb 24 at 8:41
• 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 $x=0$. Feb 24 at 9:02
• @AccidentalTaylorExpansion Airy functions are the solutions to such a potential well. Feb 24 at 9:30