A previous derivation of the single-particle Schr\"odinger equation from statistical assumptions is generalized to an arbitrary number $N$ of particles moving in three-dimensional space. Spin and gauge fields are also taken into account. It is found that the same statistical assumptions that imply Schr\"odinger's equation determine also the form of the gauge coupling terms, and the form of the corresponding local (Lorentz) forces. An explanation for the role of the electrodynamic potentials, as statistical representatives of the Lorentz force, is given. For a single particle, spin one-half is introduced as the property of a statistical ensemble to respond to an external gauge field in two different ways. A generalized calculation, using the twofold number of variables, leads to Pauli's equation. The new spin term is again the statistical representative of the corresponding local force. For a $N$ -particle system, spin is introduced as a consequence of gauge coupling.The classical limit $\hbar \to 0$ of Schr\"odinger's equation and closely related questions of interpretation of the quantum mechanical formalism are discussed.A previous derivation of the single-particle Schr\"odinger equation from statistical assumptions is generalized to an arbitrary number $N$ of particles moving in three-dimensional space. Spin and gauge fields are also taken into account. It is found that the same statistical assumptions that imply Schr\"odinger's equation determine also the form of the gauge coupling terms, and the form of the corresponding local (Lorentz) forces. An explanation for the role of the electrodynamic potentials, as statistical representatives of the Lorentz force, is given. For a single particle, spin one-half is introduced as the property of a statistical ensemble to respond to an external gauge field in two different ways. A generalized calculation, using the twofold number of variables, leads to Pauli's equation. The new spin term is again the statistical representative of the corresponding local force. For a $N$-particle system, spin is introduced as a consequence of gauge coupling.The classical limit $\hbar \to 0$ of Schr\"odinger's equation and closely related questions of interpretation of the quantum mechanical formalism are discussed.

InTech eBooksFeb 22, 20122 citations

A statistical derivation of non-relativistic quantum theory

U. Klein

A previous derivation of the single-particle Schrödinger equation from statistical assumptions is generalized to an arbitrary number $N$ of particles moving in three-dimensional space. Spin and gauge fields are also taken into account. It is found that the same statistical assumptions that imply Schrödinger's equation determine also the form of the gauge coupling terms, and the form of the corresponding local (Lorentz) forces. An explanation for the role of the electrodynamic potentials, as statistical representatives of the Lorentz force, is given. For a single particle, spin one-half is introduced as the property of a statistical ensemble to respond to an external gauge field in two different ways. A generalized calculation, using the twofold number of variables, leads to Pauli's equation. The new spin term is again the statistical representative of the corresponding local force. For a $N$ -particle system, spin is introduced as a consequence of gauge coupling.The classical limit $\hbar \to 0$ of Schrödinger's equation and closely related questions of interpretation of the quantum mechanical formalism are discussed.A previous derivation of the single-particle Schrödinger equation from statistical assumptions is generalized to an arbitrary number $N$ of particles moving in three-dimensional space. Spin and gauge fields are also taken into account. It is found that the same statistical assumptions that imply Schrödinger's equation determine also the form of the gauge coupling terms, and the form of the corresponding local (Lorentz) forces. An explanation for the role of the electrodynamic potentials, as statistical representatives of the Lorentz force, is given. For a single particle, spin one-half is introduced as the property of a statistical ensemble to respond to an external gauge field in two different ways. A generalized calculation, using the twofold number of variables, leads to Pauli's equation. The new spin term is again the statistical representative of the corresponding local force. For a $N$-particle system, spin is introduced as a consequence of gauge coupling.The classical limit $\hbar \to 0$ of Schrödinger's equation and closely related questions of interpretation of the quantum mechanical formalism are discussed.

arXiv:1109.6244Sep 28, 20111 citation

Derivation of the Schrödinger Equation

Thomas B. Andrews

Springer eBooksJan 1, 19973 citations

Eulerian and Newtonian dynamics of quantum particles

Sergey A. Rashkovskiy

We derive the classical equations of hydrodynamic type (Euler equation and the continuity equation) from which the Schrodinger equation follows as a limit case. It is shown that the statistical ensemble corresponding to quantum system and described by the Schrodinger equation, can be considered as an inviscid gas obeying the ideal gas law with quickly oscillating sign-alternating temperature. This statistical ensemble performs the complex movements consisting of smooth average movement and fast oscillations. It is shown that average movements of statistical ensemble are described by Schrodinger equation. A model of quantum motion within the limits of classical mechanics which corresponds to the considered hydrodynamic system is suggested.We derive the classical equations of hydrodynamic type (Euler equation and the continuity equation) from which the Schrodinger equation follows as a limit case. It is shown that the statistical ensemble corresponding to quantum system and described by the Schrodinger equation, can be considered as an inviscid gas obeying the ideal gas law with quickly oscillating sign-alternating temperature. This statistical ensemble performs the complex movements consisting of smooth average movement and fast oscillations. It is shown that average movements of statistical ensemble are described by Schrodinger equation. A model of quantum motion within the limits of classical mechanics which corresponds to the considered hydrodynamic system is suggested.

arXiv:1302.2502Progress of Theoretical and Experimental PhysicsJun 1, 20134 citations

The Feynman-Schrödinger equation and the method of statistical perturbations

Iosif G. Dyadkin

USSR Computational Mathematics and Mathematical PhysicsJan 1, 19680 citations

A previous derivation of the single-particle Schr\"odinger equation from statistical assumptions is generalized to an arbitrary number

N

of particles moving in three-dimensional space. Spin and gauge fields are also taken into account. It is found that the same statistical assumptions that imply Schr\"odinger's equation determine also the form of the gauge coupling terms, and the form of the corresponding local (Lorentz) forces. An explanation for the role of the electrodynamic potentials, as statistical representatives of the Lorentz force, is given. For a single particle, spin one-half is introduced as the property of a statistical ensemble to respond to an external gauge field in two different ways. A generalized calculation, using the twofold number of variables, leads to Pauli's equation. The new spin term is again the statistical representative of the corresponding local force. For a

N

-particle system, spin is introduced as a consequence of gauge coupling.The classical limit

\hbar \to 0

of Schr\"odinger's equation and closely related questions of interpretation of the quantum mechanical formalism are discussed.

A previous derivation of the single-particle Schrödinger equation from statistical assumptions is generalized to an arbitrary number

N

of particles moving in three-dimensional space. Spin and gauge fields are also taken into account. It is found that the same statistical assumptions that imply Schrödinger's equation determine also the form of the gauge coupling terms, and the form of the corresponding local (Lorentz) forces. An explanation for the role of the electrodynamic potentials, as statistical representatives of the Lorentz force, is given. For a single particle, spin one-half is introduced as the property of a statistical ensemble to respond to an external gauge field in two different ways. A generalized calculation, using the twofold number of variables, leads to Pauli's equation. The new spin term is again the statistical representative of the corresponding local force. For a

N

-particle system, spin is introduced as a consequence of gauge coupling.The classical limit

\hbar \to 0

of Schrödinger's equation and closely related questions of interpretation of the quantum mechanical formalism are discussed.