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

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.