[jeffreyH (OP)]

Take the scenario where a wave hits a knife blade edge on. How would the wave collapse be described? Does this differ from the wave hitting a flat surface?

[JP]

You're going to have to provide more information, but I assume you're talking about the quantum wave function, not a wave in general.   

We don't know how waves collapse.  What we do know is that our measurements are consistent with a theory that has waves collapsing, and we can predict when a wave will collapse depending on how it interacts with other materials.  We also know that there are explanations that don't require collapse, but predict the exact same outcomes (the pilot wave interpretation of quantum mechanics, many-worlds interpretation, etc.)  All theories have non-intuitive features, however.

The wave encountering a blade edge on will be different than the same wave encountering the flat of a blade because it is encountering a different geometry of an edge. 

[David Cooper]

I took the question to be about water waves. If one hits a vertical obstruction like a knife blade, I picture the water being forced upwards like when waves hit a harbour wall, except that water could also pass underneath it, perhaps redusing the effect. With the blade held horizontally, you could imagine the top of the wave carrying on over the top while the part below carries on below, and then the two join up again as if nothing had happened, but I'm not sure that would happen - the water is rising on the front surface of the wave rather than being pushed forwards (although it will move forward a bit too), and that upward movement would be blocked by the knife blade, so it may squirt a lot of that water out ahead and reduce the height of the wave as the wave passes the obstruction. You'd need to carry the experiment out to see what actually happens, but it might be hard to do in such a way that you can see the result clearly.

[evan_au]

A wave hitting a flat surface can be reflected ("angle of incidence=angle of reflection"), if they are not absorbed.
A wave hitting a knife edge tends to be refracted, through a wide variety of angles.

This effect is important in reducing the radar cross-section of aircraft, where most of the radar echo comes from sharp edges; creating stealth planes requires close attention to the wing and tail edges. Flat surfaces are made of absorbent material.

You can also see it in aerial photos of coastlines and harbours.

[jeffreyH (OP)]

A wave hitting a flat surface can be reflected ("angle of incidence=angle of reflection"), if they are not absorbed.
A wave hitting a knife edge tends to be refracted, through a wide variety of angles.

This effect is important in reducing the radar cross-section of aircraft, where most of the radar echo comes from sharp edges; creating stealth planes requires close attention to the wing and tail edges. Flat surfaces are made of absorbent material.

You can also see it in aerial photos of coastlines and harbours.

Thanks that is interesting information.