I Field Operator for Edge States

[thatboi]

I'm currently looking at the following set of notes and am confused at equation (1.15) where they discuss the Bogoliubov quasiparticle for the edge states. I understand up to equation (1.14), where they have solved for the edge state of the first-quantized Hamiltonian. What I don't understand is how they derived the field operator in (1.15).

 

[thatboi]

In case people are curious, see the following eqns (1.49) and (1.50) in these notes and references therein. It is a generalized real-space version of what is usually used in k-space.