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- Thread starter Silviu
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strangerep

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Since no one else has answered, here's my $0.02...Can someone explain to me what is Griffiths actually doing there?

Chapter 10 of Griffiths progresses through the following sequence:

-- The adiabatic theorem,

-- Nonholonomic systems (in which interesting measurable phenomena can happen even adiabatically, by transport around a closed loop),

-- Geometric Berry phase (which is an example of such "interesting, measurable" phenomena). He derives the geometric net phase change formula [10.49] using the adiabatic approximation back in [10.40]. See his remarks under point 3 on p338.

-- Then he gives an example of an electron in a magnetic field of constant magnitude, but changing direction, (still using the adiabatic approximation), and derives the net phase change of the electron wave function.

-- Then he moves on the A-B effect (presumably because it involves a net phase change around a closed loop, similar to geometric phase). BUT, as he notes on p348 after eq[10.95], in this case the process of going around the solenoid

I'm not sure why Griffiths does it this way. Maybe it's because the general idea of net phase change around a closed loop is easier to present at introductory level if one uses the adiabatic approximation (which simplifies some of the math). But the A-B effect, which doesn't need the adiabatic approximation, shows that net phase change around a closed loop is of far more general importance in QM,

HTH.

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