The inadmissibility of non-Stokesian vector potentials in quantum mechanics. Comments on a paper asserting the nonexistence of the Aharonov-Bohm effect

1979 ◽  
Vol 25 (2) ◽  
pp. 33-37 ◽  
Author(s):  
U. Klein
Keyword(s):  
Quantum Mechanics ◽  
Vector Potentials ◽  
Bohm Effect ◽  
Aharonov Bohm

The Aharonov-Bohm Effect and Its Applications to Magnetic Field Observation

2013 ◽  
Vol 02 (01) ◽  
pp. 26-36
Author(s):  
Akira Tonomura
Keyword(s):  
Magnetic Field ◽  
Quantum Mechanics ◽  
Gauge Fields ◽  
Observable Effect ◽  
Classical Physics ◽  
Vector Potentials ◽  
Lorentz Forces ◽  
Bohm Effect ◽  
Aharonov Bohm ◽  
Wave Properties

This article describes the Aharonov-Bohm (AB) effect of electron waves travelling in free space and its application to the observation of gauge fields (vector potentials). The AB effect is inconceivable in classical physics since an observable effect is produced on electrons passing through field-free spaces. Electrons can be affected only by Lorentz forces due to electromagnetic fields. The situation is different in quantum mechanics, where electrons show wave properties: the concept of force is no longer relevant, so electric field E and magnetic field B, defined as forces acting on a unit charge, take on secondary meanings. “Phase shifts” come into play, and the primary physical entities become neither E nor B but electrostatic potential V and vector potential A. These potentials interact with electron waves and shift their phases.

scholarly journals A general method for deriving vector potentials produced by knotted solenoids

2014 ◽  
Vol 29 (35) ◽  
pp. 1450189
Author(s):  
V. V. Sreedhar
Keyword(s):  
Magnetic Field ◽  
Charged Particles ◽  
Vector Potentials ◽  
Bohm Effect ◽  
Figure Eight Knot ◽  
Aharonov Bohm ◽  
The Magnetic Field ◽  
General Method

A general method for deriving exact expressions for vector potentials produced by arbitrarily knotted solenoids is presented. It consists of using simple physics ideas from magnetostatics to evaluate the magnetic field in a surrogate problem. The latter is obtained by modeling the knot with wire segments carrying steady currents on a cubical lattice. The expressions for a 31 (trefoil) and a 41 (figure-eight) knot are explicitly worked out. The results are of some importance in the study of the Aharonov–Bohm effect generalized to a situation in which charged particles moving through force-free regions are scattered by fluxes confined to the interior of knotted impenetrable tubes.

Analysis of Aharonov-Bohm effect due to time-dependent vector potentials

1992 ◽  
Vol 45 (7) ◽  
pp. 4319-4325 ◽  
Author(s):  
B. Lee ◽  
E. Yin ◽  
T. K. Gustafson ◽  
R. Chiao
Keyword(s):  
Time Dependent ◽  
Vector Potentials ◽  
Dependent Vector ◽  
Bohm Effect ◽  
Aharonov Bohm

TOPOLOGICAL EFFECTS IN QUANTUM MECHANICS AND HIGH VELOCITY ESTIMATES

2011 ◽  
Vol 20 (05) ◽  
pp. 951-961 ◽  
Author(s):  
RICARDO WEDER
Keyword(s):  
Exact Solution ◽  
Quantum Mechanics ◽  
Error Bounds ◽  
High Velocity ◽  
Wave Packets ◽  
Finite Energy ◽  
Time Dependent ◽  
Rigorous Proof ◽  
Bohm Effect ◽  
Aharonov Bohm

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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