Single photons traversing a beam splitter

[physmatics]

Hi!

I'm not sure this is exactly the right subforum, but here goes:

Homework Statement

So we have a source (OP) that emits single photons of a constant wavelength and angular frequency. The photons hit a 50-50 beam splitter, and are then reflected in the mirrors. Where is says (L) ou (SP) (yay for studying in French!) there is a beam splitter.

What I want to know basically is what happens. What happens when the photon hits the beam splitter? What happens at point p, and what is the probability of detecting a photon there?

Homework Equations

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The Attempt at a Solution

I think it will become a standing wave, but how does that work with only one photon? Does the photon split itself when traversing the beam splitter? What happens in that case when the two waves meet at the point p, and what is the probability of detecting a photon there?

I would be more than happy if anyone could answer this, as I haven't been able to found a similar problem anywhere and my professor refuses to answer e-mails.

Thank you so so much!

 

[physmatics]

Pardon me, it should obviously be point x instead of point p!