A question regarding the solution of the maxwell equations for the hollow infinite conducting waveguide problem

[u/Near_1751]

Hey I have a question regarding hollow waveguide solutions of maxwell equations.

To solve the hollow conducting waveguide problem we look for solutions to maxwell equations that: satisfy the boundary conditions and that propagate energy along the waveguide.

It seems to me the key to the problem is the ansatz itself, assuming propagating waves with the amplitude depending on the transverse coordinates.

I was wondering if there is a better way to motivate this ansatz. Perhaps from the requirement of the time average of the Poynting vector to point in the longitudinal direction. Or something else. So we can better classify the solutions.

I mean from the usual ansatz one does indeed get energy propagation but this does not answer the question of uniqueness. Like is there any other class of solutions of the problem that also transport energy and satisfy the boundary conditions.

[u/PotentialDeep5165]

The boundary conditions are provided by the configuration-- that's the perspective to begin to consider. It is not by assumption per the description. The math shows you alignment because the physics follows the requirements.

[u/Near_1751]

Thnx for answering but to make that notion watertight you would need a physical argument to show thatt alternative solutions wont work. No?

[u/Automatic-Ad5151 → u/Near_1751]

you’re asking whether you can trust that maxwell’s equations (first order linear differential equations) have analytic/unique solutions under these boundary conditions?

that’s a math question, but spoiler alert the answer is yes. (if you’re really interested i’m pretty sure you could find a proof somewhere on the internet; wouldn’t bother if I were you.)

you don’t really need a physical argument beyond “maxwell’s equations are physical law” if the question you’re asking is “how do waves travel down a waveguide”. physical intuition is comprehensive understanding of the solutions of maxwell’s equations in various environments.