Is there a physical meaning for where the turning points intersect with the sign change of the second derivative of a wave function? I ask because there's this picture and I think I saw something talking about it somewhere, but I don't completely understand what the point is.

Edited April 15, 201213 yr by questionposter

Is there a physical meaning for where the turning points intersect with the sign change of the second derivative of a wave function? I ask because there's this picture and I think I saw something talking about it somewhere, but I don't completely understand what the point is.

 

It is a weight of Variation End and Vanish (attenuation) End: It INDICATES here to that Tunnel, on both side - or the central well [of another case] - does have approximately, or exactly, a barabolic signature.

 

As far as I can reveal. It is a wonderful Question by the way. And, I don't think that it is a coincidence.

I think it's an artifact of the boundary conditions one applies to the problem. The wave function has to go to zero as x goes to infinity. There may also be boundary conditions placed on the derivatives at the edge of the well.