Abstract
A method is given for solving the Bogoliubov equations for quasiparticle excitations in superconductors in the WKBJ approximation. It is applied to calculate the excitation spectrum and the scattering states of an isolated vortex line in a type-II superconductor. The pair potential and magnetic field in the vicinity of the core are determined by a variational method. For values of the Ginzburg-Landau parameter $\ensuremath{\kappa}$ near 1, the energy so calculated is about 10% too high and the critical $\ensuremath{\kappa}$ for type-II superconductivity about 25% too high, indicating that the variational functions used are only approximately of the correct form. The energy of the bound states depends on the magnetic quantum number like a Landau energy; the effective magnetic field is of the order of the upper critical field ${H}_{c2}$ for all values of $\ensuremath{\kappa}$.
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