# How to solve Rashba and Dresselhaus SOC Hamiltonian

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1. Aug 31, 2015

### drFredkin

1. The problem statement, all variables and given/known data
How can I solve this hamiltonian equation?
H= p2/2m +α/ħ (σxpy - σypx) + γ/ħ (σxpx - σypy) + βxσx + βyσy

2. Relevant equations
Rashba coupling effect equation: HR=α(σykx - σxky)

3. The attempt at a solution
H02k2/2m + HR+ HD

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2. Sep 1, 2015

### hilbert2

I first thought about solving the eigenvalues and position representation eigenfunctions by assuming the eigenfunctions are of product form $\psi(x,y) = \alpha(x)\beta(y)$ and using separation of variables to get ODE:s for $\alpha$ and $\beta$, but if the coefficients $\sigma_{i}$ are matrices instead of numbers, that probably makes the situation more complicated...