I would like to find the time evolution for the given Hamiltonian, the initial state of the system we choose two spinor wavefunction ψ+(t=0) and ψ−(t=0) as given below:
The effective Hamiltonian can be written as H=νFσ⋅(q−Byˆx)
where σ=(σx,σy) and q=(qx,qy) are the Pauli matrices and the momentum operator respectively. Taking the spinor wavefunctions as ψ+=eikxψ−=eikx
as the initial condition for the Schrodinger equation. The time evolution of the system, Ψ(r,t)=e−iνFσ⋅(q−Byˆx)tΨ(r,0)
and Ψ(r,0)=eikx(11)
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