When things cannot happen (particles cannot be)

[geordief]

I understand that particles' position in space is described by a probability function that seems to me to imply that there is no part of the universe where the particle might not in theory be observed.

 

Are there in fact places and times where it is possible to say with 100% certainty that a particle will never be observed?

 

If this is the case, is there a mathematical formula to describe that circumstance (in the quantum region)?

 

 

[swansont]

I understand that particles' position in space is described by a probability function that seems to me to imply that there is no part of the universe where the particle might not in theory be observed.

 

Are there in fact places and times where it is possible to say with 100% certainty that a particle will never be observed?

 

If this is the case, is there a mathematical formula to describe that circumstance (in the quantum region)?

 

 

 

 

There are quantum solutions for an infinite square well, and the solutions are zero outside the well. But there are no real systems with infinitely high potential barriers.

[geordief]

I think the mathematical way to prove a negative (which may be what I was getting at) is to assume it is possible and to derive a contradiction from the hypothesis.

 

Can this method be applied in QM?(or used in conjunction with it)?

 

I mean I would like to be able to prove that when I sneeze ,nobody in the region of A. Centauri can possibly catch a cold.

[swansont]

I think the mathematical way to prove a negative (which may be what I was getting at) is to assume it is possible and to derive a contradiction from the hypothesis.

 

Can this method be applied in QM?(or used in conjunction with it)?

 

I mean I would like to be able to prove that when I sneeze ,nobody in the region of A. Centauri can possibly catch a cold.

 

 

 

You could show that the chance of tunneling through that barrier is ridiculously small. But it will not be identically zero.

[Country Boy]

There are situations, such as a very high, though finite, potential barrier, where the probability the particle exists is very, very low, though non-zero. You would have to decide how low that probability must be before you say "the particle is not there".

[geordief]

Are there situations where to calculate the probability would require more resources than are available in the universe?

 

Would you just say that quantum theory was inadequate but not actually wrong?