We present a method for generating wave functions for inhomogeneous superconductors. The method is based on the Andreev approximation to the Bogoliubov–de Gennes equations. Bound states for the superconductor–normal-metal–superconductor junction and the single vortex are discussed. The following simple expression for the bound-state energy as a function of the angular quantum number μ is derived: ${\mathit{E}}_{\mathrm{\mu }}$=Δ(${\mathit{r}}_{\mathrm{\mu }}$), where ${\mathit{r}}_{\mathrm{\mu }}$=μ/${\mathit{k}}_{11}$≃μ/${\mathit{k}}_{\mathit{F}}$ is the classical turning point. The agreement with recently reported exact numerical wave functions and energies is excellent.

Close

PrevNext

View figure in article