# Probability Distribution of the Time at Which an Ideal Detector Clicks

# Probability Distribution of the Time at Which an Ideal Detector Clicks

We consider a non-relativistic quantum particle surrounded by a detecting surface and ask how to compute, from the particle's initial wave function, the probability distribution of the time and place at which the particle gets detected. In principle, quantum mechanics makes a prediction for this distribution by solving the Schrodinger equation of the particle of interest together with the 10^23 (or more) particles of the detectors, but this is impractical to compute. Is there a simple rule for computing this distribution approximately for idealized detectors? I will argue in favor of a particular proposal of such a rule, the "absorbing boundary rule," which is based on a 1-particle Schrodinger equation with a certain "absorbing" boundary condition on the detecting surface. The mere existence of such a rule may seem surprising in view of the quantum Zeno effect. Time permitting, I may also be able to explain extensions of this rule to the cases of several particles, moving detectors, particles with spin, Dirac particles, curved space-time, and discrete space (a lattice). Some of the results are based on joint work with Abhishek Dhar and Stefan Teufel.