Inertio-gravity Poincaré waves and the quantum relativistic Klein-Gordon equation, near-inertial waves and the non-relativistic Schrödinger equation

E. Heifetz; Leo R.M. Maas; J. Mak; I. Pomerantz

doi:10.1063/5.0120375

Inertio-gravity Poincaré waves and the quantum relativistic Klein-Gordon equation, near-inertial waves and the non-relativistic Schrödinger equation

E. Heifetz, Leo R.M. Maas, J. Mak, I. Pomerantz

Tel Aviv University

Research output: Contribution to journal › Article › peer-review

Abstract

Shallow water inertio-gravity Poincaré 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 Schrödinger equation, and the near-inertial wave limit in the shallow water system.

Original language	English
Article number	116608
Journal	Physics of Fluids
Volume	34
Issue number	11
DOIs	https://doi.org/10.1063/5.0120375
State	Published - 1 Nov 2022

All Science Journal Classification (ASJC) codes

Condensed Matter Physics
Mechanics of Materials
Mechanical Engineering
Fluid Flow and Transfer Processes
Computational Mechanics

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10.1063/5.0120375

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title = "Inertio-gravity Poincar{\'e} waves and the quantum relativistic Klein-Gordon equation, near-inertial waves and the non-relativistic Schr{\"o}dinger equation",

abstract = "Shallow water inertio-gravity Poincar{\'e} 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 Schr{\"o}dinger equation, and the near-inertial wave limit in the shallow water system.",

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AU - Pomerantz, I.

PY - 2022/11/1

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N2 - Shallow water inertio-gravity Poincaré 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 Schrödinger equation, and the near-inertial wave limit in the shallow water system.

AB - Shallow water inertio-gravity Poincaré 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 Schrödinger equation, and the near-inertial wave limit in the shallow water system.

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M3 - مقالة

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Inertio-gravity Poincaré waves and the quantum relativistic Klein-Gordon equation, near-inertial waves and the non-relativistic Schrödinger equation

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