Question

A low-intensity beam of monoenergetic electrons is directed normally onto a wall with two narrow slits in it. The interference pattern is observed on a distant screen behind the wall. A detector is placed behind slit 2. Suppose that the effect of this detector is to randomly change the phase of the corresponding probability amplitude by 0 or \pi (i.e., it randomly multiplies the probability amplitude by +1 or −1). Show that, on average, the probability for the electron to arrive at a given point x on the screen is given by the sum of probabilities for electron to arrive at x with only slit 1 open and the probability for the electron to arrive at x with only slit 2 open (that is, the interference term averages to zero).

          A low-intensity beam of monoenergetic electrons is directed normally onto a wall with
two narrow slits in it. The interference pattern is observed on a distant screen behind
the wall. A detector is placed behind slit 2. Suppose that the effect of this detector
is to randomly change the phase of the corresponding probability amplitude by 0 or \pi 
(i.e., it randomly multiplies the probability amplitude by +1 or −1). Show that, on
average, the probability for the electron to arrive at a given point x on the screen
is given by the sum of probabilities for electron to arrive at x with only slit 1 open
and the probability for the electron to arrive at x with only slit 2 open (that is, the
interference term averages to zero).

Added by Yvonne B.

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