Talk:Pauli equation

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....

You are just talking about a different way of writing the equation. The version stated here is perfectly valid. —Preceding unsigned comment added by 84.112.160.83 (talk) 18:25, 29 October 2010 (UTC)

unfinished section

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.

Also if no-one else, I'll expand the article more. -- F = q(E + v × B) 09:27, 26 February 2012 (UTC)

Symbols for canonical and kinetic momentum

I notice that the symbols used differ from those at Momentum#Particle_in_field; maybe this should be fixed. Count Truthstein (talk) 14:42, 18 December 2012 (UTC)

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:

$i\hbar {\frac {\partial }{\partial t}}\left({\begin{array}{c}{\vec {\varphi }}_{1}\\{\vec {\varphi }}_{2}\end{array}}\right)=c\left({\begin{array}{c}{\vec {\hat {\sigma }}}{\vec {\pi }}{\vec {\varphi }}_{2}\\{\vec {\hat {\sigma }}}{\vec {\pi }}{\vec {\varphi }}_{1}\end{array}}\right)+q\phi \left({\begin{array}{c}{\vec {\varphi }}_{1}\\{\vec {\varphi }}_{2}\end{array}}\right)+mc^{2}\left({\begin{array}{c}{\vec {\varphi }}_{1}\\-{\vec {\varphi }}_{2}\end{array}}\right)$

where

${\boldsymbol {\Pi }}=\mathbf {p} -q\mathbf {A}$

is the kinetic momentum, and the following approximations are used:

• Simplification of the equation through following ansatz

$\left({\begin{array}{c}{\vec {\varphi }}_{1}\\{\vec {\varphi }}_{2}\end{array}}\right)=e^{-i{\frac {mc^{2}t}{\hbar }}}\left({\begin{array}{c}{\vec {\tilde {\varphi _{1}}}}\\{\vec {\tilde {\varphi _{2}}}}\end{array}}\right)$

• Eliminating the rest energy through an Ansatz with slow time dependence

$\partial _{t}{\vec {\tilde {\varphi _{i}}}}\ll {\frac {mc^{2}}{\hbar }}{\vec {\tilde {\varphi _{i}}}}$

• weak coupling of the electric potential

$q\phi \ll mc^{2}$

---

If we want a derivation, we should just start from scratch. M∧Ŝc²ħεИ_τlk 09:08, 5 May 2013 (UTC)

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)

I boxed the other version too. YohanN7 (talk) 12:18, 12 May 2015 (UTC)

Just a comment on your comment: Writing the equation in terms of the B-field does not prevent you from using a gauge transformation. The B-field is simply unchanged by a gauge transformation. However, with the other version boxed, I am happy. Thanks! JezuzStardust (talk)

The weak field limit and spin orbit interaction

After a quick glance I concluded that the authors are unaware that the use of total angular momentum in connection with the interaction with external magnetic field is not meaningful without simultaneously accounting for the spin orbit interaction which is not present in Pauli equation. What the authors mark weak field limit is actually strong field limit when compared with the magnitude of spin orbit interaction. As is the article is misleading if you want to fix it I can give you detailed instructions. 2001:14BA:3F2:D500:FCF5:4D76:F308:BCEC (talk) 18:54, 8 May 2023 (UTC)

Pauli equation does not contain relativistic correction terms (like spin-orbit). The equation provided also does not not seem to be strong field, strong field would have only $L_{z}+2S_{z}$. --ReyHahn (talk) 20:12, 8 May 2023 (UTC)