EM wave decomposition to axis components in the Rayleigh-Jeans cube

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SUMMARY

The discussion centers on the decomposition of electromagnetic (EM) waves into axis components within a Rayleigh-Jeans cube framework. The formulas for wavelength in the x and y directions, given as $$\lambda_x = \frac{L}{n_x}$$ and $$\lambda_y = \frac{L}{n_y}$$, highlight the challenge of fitting integer values into the cube, specifically with parameters $$n_x=4$$ and $$n_y=3$$. The necessity for the wave equation to satisfy Maxwell's equations is emphasized, alongside the boundary conditions that dictate field behavior at the cube's edges, confirming the validity of the provided formulas.

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aliinuur
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why axis components of the wave must fit as integer, but wave itseld does not?
1728648055775.png

$$\lambda_x = \frac{L}{n_x} , \lambda_y=\frac{L}{n_y} . \lambda$$
does not fit the cube as integer. In the figure
$$n_x=4, n_y=3$$
 
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I don't know what you mean exactly, but wave equation must be satisfied for the EM wave (Derived from Maxwell's equations). Boundary conditions are that the fields die at the edges, which leaves you exactly with the two formulas that you provided. (You can do for 3d case directly)
 

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