aqora

Proof of the incompleteness of wave quantum mechanics. Second part.

Субхон Джомирзоев

As a result of identifying the corpuscular-wave quantities (CWQ) of a non-relativistic electron (NE) as quantities associated with the equation of motion of wave quantum mechanics (WQM),it was discovered that WQM in reality is corpuscular-wave mechanics (CWM)and the fundamental differences between WQM and classical Newtonian mechanics (CNM) were established, and also, the possibility of creating analogies of WQM and CNM is indicated.

Dec 27, 20240 citations

Mathematical Formulation of Non-relativistic Quantum Mechanics

Valter Moretti

UnitextJan 1, 20170 citations

Spin and Madelüng fluid

Salesi, G

Starting from the Pauli current we obtain the decomposition of the non-relativistic local velocity in two parts: one parallel and the other orthogonal to the momentum. The former is recognized to be the ``classical'' part, that is the velocity of the center-of-mass, and the latter the ``quantum'' one, that is the velocity of the motion in the center-of-mass frame (namely, the internal ``spin motion'' or {\em Zitterbewegung}). Inserting the complete expression of the velocity into the kinetic energy term of the classical non-relativistic (i.e., Newtonian) Lagrangian, we straightforwardly derive the so-called ``quantum potential'' associated to the Madelung fluid. In such a way, the quantum mechanical behaviour of particles appears to be strictly correlated to the existence of spin and Zitterbewegung.Starting from the Pauli current we obtain the decomposition of the non-relativistic local velocity in two parts: one parallel and the other orthogonal to the momentum. The former is recognized to be the ``classical'' part, that is the velocity of the center-of-mass, and the latter the ``quantum'' one, that is the velocity of the motion in the center-of-mass frame (namely, the internal ``spin motion'' or {\em Zitterbewegung}). Inserting the complete expression of the velocity into the kinetic energy term of the classical non-relativistic (i.e., Newtonian) Lagrangian, we straightforwardly derive the so-called ``quantum potential'' associated to the Madelung fluid. In such a way, the quantum mechanical behaviour of particles appears to be strictly correlated to the existence of spin and Zitterbewegung.

Jul 26, 199532 citations

Mathematical formulation of non-relativistic Quantum Mechanics

Valter Moretti

UnitextJan 1, 20130 citations

On connection between classical and quantum mechanics

Daniel Sepunaru

We discuss an alternative version of non- relativistic Newtonian mechanics in terms of a real Hilbert space mathematical framework. It is demonstrated that the physics of this scheme correspondent with the standard formulation. Heisenberg-Schrodinger non-relativistic quantum mechanics is considered adequate and complete. Since the suggested theory is dispersion free, linear superposition principle is not violated but cannot affect results of measurements due to spectral decomposition theorem for self-adjoint operators (the collapse of wave function).We discuss an alternative version of non- relativistic Newtonian mechanics in terms of a real Hilbert space mathematical framework. It is demonstrated that the physics of this scheme correspondent with the standard formulation. Heisenberg-Schrodinger non-relativistic quantum mechanics is considered adequate and complete. Since the suggested theory is dispersion free, linear superposition principle is not violated but cannot affect results of measurements due to spectral decomposition theorem for self-adjoint operators (the collapse of wave function).

arXiv:quant-ph/0606121Jun 14, 20060 citations

Relativistic and Non-Relativistic Quantum Mechanics

Luis Grave de Peralta, Maricela Fernández Lozada, Hira Farooq +3 more

Undergraduate lecture notes in physicsJan 1, 20230 citations

The borderland between quantum and classical mechanics

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