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It's been awhile since I've dealt with quantum mechanics (QM), but I didn't study much (if at all) about relativity and QM together.  I think, in general the two theories don't work well together.

 

I'm not sure if there are any members here studying Physics.

 


 

If Q is an object and the object is moving, then the object is contracted along the direction of motion.  This means the volume shrinks.  If Q is a region of space, it is not affected by motion so it's not flattened.

 

I'm not sure how well wave functions work with Special Relativity, so I just don't know how to answer that question.

 

Since the wave functions described the probability of finding a particle (even a large object), according to QM, and the object is length contracted, I would have to assume the wave function describing a particle (or object) has to change with increasing velocity.  However, I'm really not clear on what you're asking.  :)