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Abstract <p> In this note, we show that the Schrödinger equation in quantum mechanics is mathematically equivalent to the Euler-Bernoulli equation for vibrating beams and plates in elasticity theory, with dependent initial data. Remarks are made on potential applications of this equivalence for symplectic and quantum computing, the two-slit experiment using vibrating beams and plates, and the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12607_2025_1113_Article_IEq1.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">\(p\)</EquationSource> </InlineEquation>-adic Euler-Bernoulli equation. </p>

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On the Equivalence Between the Schrödinger Equation in Quantum Mechanics and the Euler-Bernoulli Equation in Elasticity Theory

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • Igor V. Volovich

摘要

Abstract

In this note, we show that the Schrödinger equation in quantum mechanics is mathematically equivalent to the Euler-Bernoulli equation for vibrating beams and plates in elasticity theory, with dependent initial data. Remarks are made on potential applications of this equivalence for symplectic and quantum computing, the two-slit experiment using vibrating beams and plates, and the \(p\) -adic Euler-Bernoulli equation.