we neglect the vector potential which is known to give only a moderate renormalization of the interlevel spacing $\omega$ (see Ref. ).

Spectrum and local density of states {#sec:results}
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Vortex molecules {#subsec:molecules}
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We now proceed with the calculation of LDOS profiles for two systems: (i) vortex–vortex pair and (ii) vortex positioned near the flat superconducting boundary. The image method discussed in Ref.  allows us to show that the latter case is equivalent to the vortex-antivortex pair in the bulk provided we choose the distance between the vortex and antivortex to be two times larger than the distance from the vortex to the flat surface in the original problem. To elucidate our main results we start from a qualitative description of the quasiparticle spectra following Ref. .

Let us consider two vortices oriented along the $z$ axis. In the plane $(xy)$ the corresponding phase singularity points (or vortex centers) are positioned at ${\bf r}_{1,2}=(\pm a/2,0)$. For quasiparticles propagating along the classical trajectories parallel to ${\bf k}_F$ we introduce the angular momenta $\mu=[{\bf r},{\bf k}_F]\cdot{\bf z_0}=k_F
r\sin(\theta_p-\theta)$ and $\tilde\mu_i=\mu-[{\bf r}_i,{\bf
k}_F]\cdot{\bf z}_0$ defined with respect to the $z$–axis passing through the origin and with respect to the $i$-th vortex axis 