Euler’s Mechanics and Schrödinger’s Quantum Mechanics

D. Suisky

Ahmad Zareei

Here we present a transformation that maps the Schrodinger equation of quantum mechanics to the incompressible Euler equations of fluid mechanics. The transformation provides a wave solution and a potential function based on fluid properties that satisfy the Schrodinger equation given that the fluid velocity potential and pressure satisfy the Euler equations. Interestingly, in our transformation, the equivalent of quantum potential becomes the physical surface tension. This is contrary to the Madelung transformation that maps the Schrodinger equation to the compressible Euler equations where there is no physical counterpart for the quantum potential. Lastly, we show that using this transformation, the Bohm equation can be mapped to a particle's equation of motion moving on the free surface of the fluid.

акустика Механика

Igor Vasil'evich Volovich

In this note, we show that the Schrodinger 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.

Francesco R. Ruggeri

It is interesting to note that d/dx [ln(d(x))] where d(x) is the spatial density, plays a central role in the time-independent Schrodinger equation, classical mechanics, the Euler equation, equilibrium statistical mechanics and Brownian motion and in all cases, even the quantum one, is related to force as -d/dx V(x), where V(x) is the potential. In this note, we try to examine the role of d/dx [ln(d(x))], and in particular try to see how quantum mechanics is related to classical and fluid mechanics and how it differs.

Alexander Komech