Wavefunction is essentially a single particle concept. It is easily extended to multiparticle system as follows- if one has say five electrons the wavefunction of this five electron state is any completely antisymmetric function of five coordinates which is square integrable in the five dimensional space. Given a five electron ket in fock space $|K\rangle$, its wavefunction is denoted as $\langle x_1 x_2 ...x_5|K\rangle$. But for a superconductor its effective Hamiltonian doesn't conserve the particle number. Then can one come up with any reasonable defination of a wavefunction for a single quasiparticle excitation of the superconductor over its ground state denoted by $\gamma_i^{\dagger} |G\rangle$ where $|G\rangle$ is superconducting groundstate composed of Cooper pairs and $\gamma_i^{\dagger}=\sum_k u_i^kc_k+v_i^kc_k^{\dagger}$ is Bogoliubov quasiparticle creation operator and $c's$ being electron operators and $u's$ and $v's$ being some complex numbers.

In Kitaev chain and it's solid state realisation one usually talks about Majorana fermion(Bogoliubov excitation) being localised at the two ends. How can one do that without a reasonable definition of wavefunction for superconducting states? The papers usually interpret eigenvectors of $H_{BdG}$ in coordinate space as representative wavefunctions. Is it justified?

This post imported from StackExchange Physics at 2015-02-15 12:14 (UTC), posted by SE-user Noob Rev B