- #1
maverick280857
- 1,789
- 4
The regular spin orbit Hamiltonian is
[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?
[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?