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## Homework Statement

Suppose that we have a source of particles (e.g. photons) S, then three slits labelled 1,2 and 3, followed by a screen. For a particle that has passed through slit i, where i=1,2,3, let ψ

_{i}(x) be the amplitude for the particle arriving at a position x units along the screen.

(a) Write down the probability density function for detecting a particle at a position x on the screen when:

1. all three slits are open,

2. slits 1 and 3 are open,

[Note: you don't need to determine explicit expressions for the amplitudes ψ

_{i}(x)]

(b) If we applied purely classical physics, how would your answers to the above differ?

(c) Suppose we know the probability density functions for detecting the particle at a position x when only one particular slit is open. That is, we know P

_{1}(x), P

_{2}(x) and P

_{3}(x). Are we able to express the probability density function for the case of all three slits open in terms of P

_{1}(x), P

_{2}(x) and P

_{3}(x)? Can we do this if we apply purely classical physics?

## Homework Equations

## The Attempt at a Solution

(a) |ψ

_{slits 1,2,3}|

^{2}= (ψ*

_{slit 1}+ ψ*

_{slit 2}+ ψ*

_{slit 3})(ψ

_{slit 1}+ ψ

_{slit 2}+ ψ

_{slit 3})

= |ψ

_{slit 1}|

^{2}+ |ψ

_{slit 2}|

^{2}+ |ψ

_{slit 3}|

^{2}+ ψ*

_{slit 1}ψ

_{slit 2}+ ψ*

_{slit 1}ψ

_{slit 3}+ ψ*

_{slit 2}ψ

_{slit 1}+ ψ*

_{slit 2}ψ

_{slit 3}+ ψ*

_{slit 3}ψ

_{slit 1}+ ψ*

_{slit 3}ψ

_{slit 2}

(b) The probability density functions would add linearly in classical physics, giving:

|ψ

_{slits 1,2,3}|

^{2}= |ψ

_{slits 1}|

^{2}+ |ψ

_{slits 2}|

^{2}+ |ψ

_{slits 3}|

^{2}

(c) Well I would just plug the values for P(x) into the above equations for QM and classical physics, respectively, right?