Introduction

We consider the two basic theories of the standard physics: (1) the theory

of relativity, as a four-dimensional time-space description of our universe, with the

invariance of the time-space interval which leads to the Lorentz transformation, and

(2) quantum mechanics, based on the Schrödinger equation, with a solution called

wave function. However, we find that this equation is very unsatisfactory, describing

fully unlocalized free particles, any initially localized particle rapidly spreading in

space, in disagreement with the fundamental Hamilton equations. In agreement with

the Hamilton equations, we describe a quantum particle by propagation wave

functions in the coordinate and momentum spaces, with the Lagrangian in the time

dependent phase instead of the Hamiltonian coming from the Schrödinger equation.

With the relativistic Lagrangian, we obtain wave functions describing invariant

distributions propagating in space.

Keywords: Light velocity, Time-space interval, Lorentz transformation, Hamiltonian, Kinetic energy, Potential energy, Mass, Schrödinger equation, Operator, Heisenberg picture, Schrödinger picture, Hamilton equation, Wave function, Wave packet, Group velocity, Standard deviation, Mean value, Commutation, Lagrangian, Proper time, Momentum, Conjugate space, Metric tensor.

Cite as

Current Physics

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Digital Signal Processing in Experimental Research

Frontiers in Nuclear and Particle Physics

Advances in Classical Field Theory

Progress in Computational Physics (PiCP)

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Transport Phenomena In Particulate Systems

Topological Geometrodynamics

DOI https://doi.org/10.2174/9789815051094122030003	Print ISSN 2542-5064
Publisher Name Bentham Science Publisher	Online ISSN 2542-5072

Open Quantum Physics and Environmental Heat Conversion into Usable Energy