2022
DOI: 10.1063/5.0120375
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Inertio-gravity Poincaré waves and the quantum relativistic Klein–Gordon equation, near-inertial waves and the non-relativistic Schrödinger equation

Abstract: Shallow water inertio-gravity Poincare waves in a rotating frame satisfy the Klein-Gordon equation, originally derived for relativistic, spinless quantum particles. Here we compare these two superficially unrelated phenomena, suggesting a reason for them sharing the same equation. We discuss their energy conservation laws and the equivalency between the non-relativistic limit of the Klein-Gordon equation, yielding the Schrodinger equation, and the near-inertial wave limit in the shallow water system.

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