Nonequivalent representations of canonical commutation relations in quantum mechanics: The case of the Aharonov-Bohm effect

2007 ◽  
Vol 75 (3) ◽  
pp. 268-271 ◽  
Author(s):  
Luciano Bracci ◽  
Luigi E. Picasso
Keyword(s):  
Quantum Mechanics ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
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.

Can elementary quantum mechanics explain the Aharonov–Bohm effect?

1995 ◽  
Vol 36 (1) ◽  
pp. 177-186 ◽  
Author(s):  
C. Magni ◽  
F. Valz‐Gris
Keyword(s):  
Quantum Mechanics ◽  
Bohm Effect ◽  
Aharonov Bohm
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