An empirical and classical approach for nonperturbative, high velocity, quantum mechanics

We consider the problem of obtaining high-velocity estimates for finite energy solutions (wave packets) to Schrödinger equations for N-body systems. We discuss a time-dependent method that allows us to obtain precise estimates with error bounds that decay as a power of the velocity. We apply this method to the electric Aharonov–Bohm effect. We give the first rigorous proof that quantum mechanics predicts the existence of this effect. Our result follows from an estimate in norm, uniform in time, that proves that the Aharonov–Bohm Ansatz is a good approximation to the exact solution to the Schrödinger equation for high velocity.

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An Entropic Dynamics Approach to Geometrodynamics

Proceedings ◽

10.3390/proceedings2019033013 ◽

2019 ◽

Vol 33 (1) ◽

pp. 13

Author(s):

Selman Ipek ◽

Ariel Caticha

Keyword(s):

General Relativity ◽

Quantum Mechanics ◽

Quantum Theory ◽

First Principles ◽

Scalar Fields ◽

Poisson Brackets ◽

Classical Approach ◽

Quantum Domain ◽

Physical Information ◽

Entropic Dynamics

In the Entropic Dynamics (ED) framework quantum theory is derived as an application of entropic methods of inference. The physics is introduced through appropriate choices of variables and of constraints that codify the relevant physical information. In previous work, a manifestly covariant ED of quantum scalar fields in a fixed background spacetime was developed. Manifest relativistic covariance was achieved by imposing constraints in the form of Poisson brackets and of intial conditions to be satisfied by a set of local Hamiltonian generators. Our approach succeeded in extending to the quantum domain the classical framework that originated with Dirac and was later developed by Teitelboim and Kuchar. In the present work the ED of quantum fields is extended further by allowing the geometry of spacetime to fully partake in the dynamics. The result is a first-principles ED model that in one limit reproduces quantum mechanics and in another limit reproduces classical general relativity. Our model shares some formal features with the so-called “semi-classical” approach to gravity.

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On the Semi-classical Approach to the Physical Axiomatic of Quantum Mechanics and the New Wave-Particle Interpretation of Light

American Journal of Modern Physics ◽

10.11648/j.ajmp.20200903.12 ◽

2020 ◽

Vol 9 (3) ◽

pp. 48

Author(s):

Andrei Nechayev

Keyword(s):

Quantum Mechanics ◽

Classical Approach ◽

New Wave ◽

Particle Interpretation

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Galactic orbits of stars

Symposium - International Astronomical Union ◽

10.1017/s0074180900105340 ◽

1966 ◽

Vol 25 ◽

pp. 93-97

Author(s):

Richard Woolley

Keyword(s):

Globular Cluster ◽

Potential Field ◽

High Velocity ◽

Velocity Vector ◽

Variable Stars ◽

The Sun ◽

Proper Motions ◽

Rr Lyrae ◽

The Galaxy

It is now possible to determine proper motions of high-velocity objects in such a way as to obtain with some accuracy the velocity vector relevant to the Sun. If a potential field of the Galaxy is assumed, one can compute an actual orbit. A determination of the velocity of the globular clusterωCentauri has recently been completed at Greenwich, and it is found that the orbit is strongly retrograde in the Galaxy. Similar calculations may be made, though with less certainty, in the case of RR Lyrae variable stars.

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Supernovae and interstellar gas dynamics

Symposium - International Astronomical Union ◽

10.1017/s0074180900100774 ◽

1967 ◽

Vol 31 ◽

pp. 117-119

Author(s):

F. D. Kahn ◽

L. Woltjer

Keyword(s):

Lower Limit ◽

High Velocity ◽

Gas Dynamics ◽

Interstellar Cloud ◽

Interstellar Gas ◽

Random Motions ◽

Relativistic Particles

The efficiency of the transfer of energy from supernovae into interstellar cloud motions is investigated. A lower limit of about 0·002 is obtained, but values near 0·01 are more likely. Taking all uncertainties in the theory and observations into account, the energy per supernova, in the form of relativistic particles or high-velocity matter, needed to maintain the random motions in the interstellar gas is estimated as 1051·4±1ergs.

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