I try diagonalize the Hamiltonian for a 1D wire with proximity-induced superconductivity. In the case without a superconductor is all fine. However, with a superconductor I don't get the correct result for the energy spectrum of the Hamiltonian (arxiv:1302.5433)(adsbygoogle = window.adsbygoogle || []).push({});

[itex]H=\eta(k)τz+Bσ_x+αkσ_yτ_z+Δτ_x[/itex]

Here σ and τ are the Pauli matrices for the spin and particle-hole space.

Now the correct result is: [itex]E^2(k)=Δ^2+η^2(k)+B^2+(αk)^2 ± \sqrt{B^2Δ^2+η^2(k)B2+η^2(k)(αk)^2}[/itex]

My problem is now that I don't know how I bring the Hamiltonian in the correct matrix form for the calculation of the eigenvalues. If i try it with the upper Hamiltonian I have completely wrong results for the energy spectrum. I believe my mistake is the interpretation of the Pauli matrices τ but I don't know how I can write the Hamiltonian in the form to get the correct eigenvalues.

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# Diagonalization of a hamiltonian for a quantum wire

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