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The first two versions of the Pauli equations given in this article is wrong I think. The sigma matrices should not appear where it is. Instead there should be a term proportional to sigma cdot B, where B is the B-field. I have tried to look at the form given here and tried to derive this equation from it but failed....
The last section needs completion and clarity. I tried myself and didn't change it. If a source can be found for the derivation I'll add it in time if no-one else does.
Symbols for canonical and kinetic momentum
Removal of content
In addition to cleanup/correcting bits I removed the completely unsourced and unclear section:
Derivation of the Pauli equation by Schrödinger
The Dirac equation for weak electromagnetic interactions is the starting point:
is the kinetic momentum, and the following approximations are used:
- Simplification of the equation through following ansatz
- Eliminating the rest energy through an Ansatz with slow time dependence
- weak coupling of the electric potential
Strange formatting of the first equation
The first equation is written in a very strange form. Even though it works mathematically, there is no physical reason to combine the Pauli matrix terms with the kinetic energy operator. This is not the way Pauli wrote it in his original paper and this form is not the standard way of writing the equation. It does occur in one of the references (Bransden & Jochain) but only as a step in the derivation of the final equation. So for both historical reasons and to adhere to standard notation I strongly oppose displaying and boxing in the first equation. Furthermore, the statement "(General)" within the box suggest that this is the main form of the equation and that the form with a magnetic field is not as general, while they are in fact equivalent.
- The "general form" has a more uniform appearance than the other form that mixes potentials A and field strengths B (which is kind of unnatural and potentially misleading). Besides, you can play around with gauge transformations in the "general form", but not in the other. Comparison with the Dirac equation is straightforward in the "general form", but not in the other. But I don't feel strongly about this. YohanN7 (talk) 11:54, 12 May 2015 (UTC)