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

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The discussion focuses on the decomposition of electromagnetic (EM) waves into axis components within a Rayleigh-Jeans cube framework. It highlights the relationship between wavelength and integer values for the cube dimensions, specifically noting that λ does not fit as an integer. The wave equation, derived from Maxwell's equations, must be satisfied, with boundary conditions requiring that fields diminish at the edges. The provided formulas for λ_x and λ_y correspond to specific integer values for n_x and n_y. The conversation suggests that a similar approach can be applied directly to three-dimensional cases.
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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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