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How to solve Rashba and Dresselhaus SOC Hamiltonian

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  1. Aug 31, 2015 #1
    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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  3. Sep 1, 2015 #2

    hilbert2

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    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...
     
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