Understanding the Born Rule for Continuous Particle Position Measurement"

[nomadreid]

If I have the formulation right, the Born rule says that the probability that a measurement for the position of the particle at time t will be in the real interval [a,b] equals ∫_a^b|ψ(x,t)|²dx. Fine. So, is the probability that a continuous measurement for the position of the particle will be in the real interval [a,b] at least once during the time interval [t1,t2] just equal to ∫_t1^t2∫_a^b|ψ(x,t)|²dx dt, or does this not work? If not, is there a more appropriate calculation?

 

[bhobba]

So, is the probability that a continuous measurement

That's the quantum zeno effect which is something rather interesting:
http://en.wikipedia.org/wiki/Quantum_Zeno_effect

Thanks
Bill

 

[atyy]

Here's a review of continuous measurements http://arxiv.org/abs/quant-ph/0611067, and a discussion of how it relates to the quantum Zeno effect http://arxiv.org/abs/1009.4968. There are several ways of looking at the quantum Zeno effect as discussed in http://arxiv.org/abs/0903.3297.

 

[nomadreid]

Thanks, bhobba and atyy. Never considered that! Fascinating...