What Is the Role of Symmetry in the Double Slit Experiment?

[nickap34]

Homework Statement

Consider the double-slit experiment with electrons (quantum particles) as discussed in class.
Denote point M on the detector screen as directly opposite the midpoint between the two slits.
Additionally, the probability of an electron striking M if slit 2 is closed is P1 = p.
(a) What is the probability P2 of an electron striking M if slit 1 is closed? [Hint: Invoke symmetry.]
(b) What would be the probability of an electron striking M if both slits were open, but the slit
through which each electron passed is detected? Explain your reasoning.
(c) What is the probability amplitude of an electron striking the point M if both slits are open but
the slit through which the electrons pass is not detected. Hence show that in this case, the
probability of an electron reaching the point M is increased as compared to part (b), and
determine by what factor this probability is increased.
(d) At a second point M0
close to M, it is found that to a good approximation, the values of P1
and P2 are the same as their values at M. However, with both slits open, no electrons are observed
to strike M0
. How can this be possible?

Relevant Equations

None

I have no clue how to answer this question. I would imagine for (a) that half of the probability of total particles goes away with only one slit.

 

[mfb]

I would imagine for (a) that half of the probability of total particles goes away with only one slit.

Half the probability of what?

You are not considering both slits at the same time in (a), you are just considering individual slits. If only slit 1 is open your chance to detect the particle there is p. If only slit 2 is open, what is the chance to detect the particle there?
The problem statement tells you to consider the symmetry of the question.

Are you familiar with the double-slit experiment with light? Because all the answers would be the same if you replace electrons with photons.