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Home Modern Physics Light as a Particle Examples What is the proportionality constant?  
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What is the proportionality constant?What is the proportionality constant that would make an actual equation out of (probability distribution) (amplitude)^{2}? The probability that the photon is in a certain small region of volume v should equal the fraction of the wave's energy that is within that volume:
We assume v is small enough so that the electric and magnetic fields are nearly constant throughout it. We then have
We can simplify this formidable looking expression by recognizing that in an electromagnetic wave, E and B are related by E = cB. With some algebra, it turns out that the electric and magnetic fields each contribute half the total energy, so we can simplify this to
As advertised, the probability is proportional to the square of the wave's amplitude.


Home Modern Physics Light as a Particle Examples What is the proportionality constant? 