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I am currently reading page 20 of Townsend's Quantum Physics book. Here are a few sentences that I am unsure of:

"In general, the magnitude and phase of the probability amplitude are determined from first principles by solving Maxwell's equations. In free space, these equations can be reduced to the wave equation (1.9)."

Equation (1.9) is [itex]\displaystyle \frac{\partial^2 E}{\partial x^2} - \frac{1}{c^2} \frac{\partial^2 E}{\partial t^2} = 0[/itex]

What are these first principles to which the author alludes; and which equations can be reduced to equation (1.9)?

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# Probability Amplitude Maxwell's Equations

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