- #1

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[tex]H_{SO} = \frac{q\hbar}{4 m^2 c^2}\sigma\cdot(\textbf{E}\times \textbf{p})[/tex]

If I consider a 2D system where E = E(x,y) and p is treated as an operator, i.e. [itex]\hat{p} = \hat{i}p_x + \hat{j}p_y[/itex] then, clearly E and p do not commute, so this doesn't look like a Hermitian operator.

Shouldn't this be added to its Hermitian adjoint (and divided by 2) to get a Hermitian Hamiltonian?