Question

Consider the experiment in the figure _a double double- slit experiment. A particle may take four paths from the source S to a point X on the detector scrcen. The paths have the following amplitudes Path 1: S→A→1→X pi 10 Path 2: S→B→1→X 10 Path 3: S→A→2→X Path 4: S→B→2→X 2 There are four different ways to perform the experiment the method used affects the probability of detccting a par- ticle at x. (a) The experiment is performed so that it is not possible to determine which hole in the first screen (A or B) a particle passes through, and it is not possible to determine which hole in the second screen (1 or 2) the particle passes through. What is the probability of detecting a particle at X? (b) The experiment is performed so that it is possible to determine which hole in the first screen (A or B) a particle passes through, and it is possible to determine which hole in the second screen (1 or 2) the particle passes through. What is the probability of detecting a particle at X? (c) The experiment is performed so that it is not possible to determine which hole in the first screen (A or B) a particle passes through, but it is possible to determine which hole in the second screen (1 or 2) the particle passes through. What is the probability of detecting a particle at X? (d) The experiment is performed so that it is possible to determine which hole in the first screen (A or B) a particle passes through, but it is not possible to determine which hole in the second screen (1 or 2) the particle passes through. What is the probability of detecting a particle at X?

Answer 1

0 Solrlion Given that tO Path 4' oalized base of Ihe a) let φ, , φ2 ,V3,Pu be the patb t,2,3 and Particle «ohrle moving hrough tat pat uestihatwe is going to choose (as caïd in bot heist ad he Seond screens So the probability of tinding -the porticle at Σ N NY

Th en Lwe knoior both the scren ro the Parttcle Pa oherete Can ake an onc co uo ave Junction ike Pah 2 Se te Prababi lity ttte Partiek n g Other Thie o behe Same -Jre athe olhe 3 Pa-the