Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physics Essays

Derivation of Schrödinger equation from the laws of classical mechanics, structures in physical vacuum

Nina B. Sotina

Published Sep 16, 2014• 3 citations
Publisher
DOI
10.4006/0836-1398-27.3.321

Related papers

The Conversion between Schrödinger Equation and F=ma

Runsheng Tu

The compatibility between quantum mechanics and classical mechanics is always worth discussing. Schrödinger equation (SE) can be derived from F=ma and T+V=E. Important classical physics formulas can be derived from the SE. The SE intuitively contains the mass m and the potential energy formula (this quality m can be large enough to enter the macro range and the potential energy comes from classical attraction). These three points determine that the SE is an organic combination of wave functions and classical mechanical laws. Based on this, it can be predicted that the SE, which can be used to describe macroscopic objects, can be established. It can be observed from the experiment of electron diffraction in a magnetic field that the volatility and property of moving electrons can be presented simultaneously. This experimental phenomenon, together with the mathematical analysis mentioned above, supports the conclusion that Newton's second law still applies in the microscopic world. According to the SE, it can be proven that "the energy of a moving particle described by the law of waves is equivalent to a multiple of its kinetic energy"; There is no absolute boundary between macro and micro (or classical and quantum), and they can be compatible.

Applied sciences research periodicals.•Feb 3, 2026•1 citation

On the derivation of the Schrödinger equation from Newtonian mechanics

Julio Alfonso Alonso, M. Paz Nieto, Emilio Santos

Physics Letters A•Mar 1, 1972•20 citations

Schrödinger: The Brilliant Plumber Quantum Mechanics as Vacuum Hydrodynamics in the 23-Channel Structured Space

ALFREDO LUIS ACOSTA PADILLA

We demonstrate that the Schrödinger equation is not a fundamental axiom of quantum mechanics but rather the linearized Navier-Stokes equation for torsion flow in a 23-channel structured vacuum. Schrödinger, like a brilliant plumber, discovered the correct equations for how "something" flows through the vacuum's pipes—but without knowing what that something was. Born and Bohr later convinced the world that nothing actually flows, and that ψ represents only "probability amplitude"—thus creating an artificial mystery and abandoning physical reality. We restore the water to the pipes: ψ is the local torsion of the pre-geometric tensor field Ξ_μν, |ψ|² is energy density, e^(iθ) is the helical rotation angle in channel 23, and the "probability current" j is actual hydrodynamic flow. All quantum "mysteries" (wave function collapse, superposition, tunneling, entanglement, uncertainty) emerge naturally from vacuum hydrodynamics without additional postulates. Quantum mechanics is not probabilistic—it is geometric fluid dynamics in disguise. We derive the Schrödinger equation from first principles, reinterpret all standard quantum phenomena as fluid behavior, and provide testable predictions distinguishing this framework from Copenhagen orthodoxy. Key results: (1) ψ = vacuum torsion field (physical, not probabilistic), (2) Schrödinger equation derived from Navier-Stokes, (3) quantum potential = pressure gradient, (4) momentum operator = helical screw geometry, (5) collapse = vortex stabilization at speed c, (6) entanglement = shared channel topology, (7) testable predictions: crystalline anisotropy (4% effect), vacuum viscosity (decoherence limit), propagation delays in entanglement. This work completes the demolition of Copenhagen interpretation and restores physical realism to quantum mechanics. The brilliant plumber (Schrödinger) gave us the pipes. We give you the blueprint.

•Jan 1, 2026•0 citations

Derivation of the Schrödinger Equation

Thomas B. Andrews

Springer eBooks•Jan 1, 1997•3 citations

From Classical Hamiltonian Flow to Quantum Theory: Derivation of the Schrödinger Equation

Gerhard Grössing

arXiv:quant-ph/0311109•Foundations of Physics Letters•Jul 22, 2004•34 citations

Quantum Mechanics and Classical Mechanics Can Be Used Together

Runsheng Tu

Quantum mechanics and classical mechanics are incompatible, and the highly controversial concepts of "uncertainty" and "non realism" are deeply rooted old ideas. Their existence has seriously hindered the development of physics. It is the obligation of explorers to clarify the reasons, methods, application examples, and significance of combining quantum mechanics with classical mechanics. By analyzing the composition, structure, and function of the Schrödinger equation, it can be concluded that the equation itself is a product of the organic combination of classical mechanical laws and wave functions. Prove that the Schrödinger equation is an organic synthesis of the classical mechanical law T+V=E and the wave function (including its differential). Export the Schrödinger equation with gravitational potential energy that can describe macroscopic systems. Pure mathematical methods cannot limit the magnitude of the mass m in the Schrödinger equation. These three facts determine that classical mechanics and quantum mechanics can be used simultaneously to describe the same object that is not limited by mass (providing multiple successful computational examples of "simultaneous use"). These research conclusions can lead to conceptual innovation, theoretical innovation, methodological innovation, and knowledge renewal in physics.

Advances in Theoretical & Computational Physics•Oct 8, 2025•1 citation
The compatibility between quantum mechanics and classical mechanics is always worth discussing. Schrödinger equation (SE) can be derived from F=ma and T+V=E. Important classical physics formulas can be derived from the SE. The SE intuitively contains the mass m and the potential energy formula (this quality m can be large enough to enter the macro range and the potential energy comes from classical attraction). These three points determine that the SE is an organic combination of wave functions and classical mechanical laws. Based on this, it can be predicted that the SE, which can be used to describe macroscopic objects, can be established. It can be observed from the experiment of electron diffraction in a magnetic field that the volatility and property of moving electrons can be presented simultaneously. This experimental phenomenon, together with the mathematical analysis mentioned above, supports the conclusion that Newton's second law still applies in the microscopic world. According to the SE, it can be proven that "the energy of a moving particle described by the law of waves is equivalent to a multiple of its kinetic energy"; There is no absolute boundary between macro and micro (or classical and quantum), and they can be compatible.
We demonstrate that the Schrödinger equation is not a fundamental axiom of quantum mechanics but rather the linearized Navier-Stokes equation for torsion flow in a 23-channel structured vacuum. Schrödinger, like a brilliant plumber, discovered the correct equations for how "something" flows through the vacuum's pipes—but without knowing what that something was. Born and Bohr later convinced the world that nothing actually flows, and that ψ represents only "probability amplitude"—thus creating an artificial mystery and abandoning physical reality. We restore the water to the pipes: ψ is the local torsion of the pre-geometric tensor field Ξ_μν, |ψ|² is energy density, e^(iθ) is the helical rotation angle in channel 23, and the "probability current" j is actual hydrodynamic flow. All quantum "mysteries" (wave function collapse, superposition, tunneling, entanglement, uncertainty) emerge naturally from vacuum hydrodynamics without additional postulates. Quantum mechanics is not probabilistic—it is geometric fluid dynamics in disguise. We derive the Schrödinger equation from first principles, reinterpret all standard quantum phenomena as fluid behavior, and provide testable predictions distinguishing this framework from Copenhagen orthodoxy. Key results: (1) ψ = vacuum torsion field (physical, not probabilistic), (2) Schrödinger equation derived from Navier-Stokes, (3) quantum potential = pressure gradient, (4) momentum operator = helical screw geometry, (5) collapse = vortex stabilization at speed c, (6) entanglement = shared channel topology, (7) testable predictions: crystalline anisotropy (4% effect), vacuum viscosity (decoherence limit), propagation delays in entanglement. This work completes the demolition of Copenhagen interpretation and restores physical realism to quantum mechanics. The brilliant plumber (Schrödinger) gave us the pipes. We give you the blueprint.
Quantum mechanics and classical mechanics are incompatible, and the highly controversial concepts of "uncertainty" and "non realism" are deeply rooted old ideas. Their existence has seriously hindered the development of physics. It is the obligation of explorers to clarify the reasons, methods, application examples, and significance of combining quantum mechanics with classical mechanics. By analyzing the composition, structure, and function of the Schrödinger equation, it can be concluded that the equation itself is a product of the organic combination of classical mechanical laws and wave functions. Prove that the Schrödinger equation is an organic synthesis of the classical mechanical law T+V=E and the wave function (including its differential). Export the Schrödinger equation with gravitational potential energy that can describe macroscopic systems. Pure mathematical methods cannot limit the magnitude of the mass m in the Schrödinger equation. These three facts determine that classical mechanics and quantum mechanics can be used simultaneously to describe the same object that is not limited by mass (providing multiple successful computational examples of "simultaneous use"). These research conclusions can lead to conceptual innovation, theoretical innovation, methodological innovation, and knowledge renewal in physics.