- #1
IanBerkman
- 54
- 1
Dear all,
The Hamiltonian for a spin-orbit coupling is given by:
[tex]
\mathcal{H}_1 = -\frac{\hbar^2\nabla^2}{2m}+\frac{\alpha}{2i}(\boldsymbol \sigma \cdot \nabla + \nabla \cdot \boldsymbol \sigma)
[/tex]
Where
[tex]
\boldsymbol \sigma = (\sigma_x, \sigma_y, \sigma_z)
[/tex]
are the Pauli-matrices.
I have to find the eigenfunctions of this equation. However, I am not sure how to interpret the part: [tex]
\nabla \cdot \boldsymbol \sigma [/tex]
The Pauli-matrices are 2x2 matrices containing only constants, does this mean this term equals zero?
Thanks in advance.
Ian
The Hamiltonian for a spin-orbit coupling is given by:
[tex]
\mathcal{H}_1 = -\frac{\hbar^2\nabla^2}{2m}+\frac{\alpha}{2i}(\boldsymbol \sigma \cdot \nabla + \nabla \cdot \boldsymbol \sigma)
[/tex]
Where
[tex]
\boldsymbol \sigma = (\sigma_x, \sigma_y, \sigma_z)
[/tex]
are the Pauli-matrices.
I have to find the eigenfunctions of this equation. However, I am not sure how to interpret the part: [tex]
\nabla \cdot \boldsymbol \sigma [/tex]
The Pauli-matrices are 2x2 matrices containing only constants, does this mean this term equals zero?
Thanks in advance.
Ian