  The energy spectrum and the eigenstates of a rectangular quantum dot
containing soft potential walls in contact with a superconductor are calculated
by solving the Bogoliubov-de Gennes (BdG) equation. We compare the quantum
mechanical solutions with a semiclassical analysis using a Bohr--Sommerfeld
(BS) quantization of periodic orbits. We propose a simple extension of the BS
approximation which is well suited to describe Andreev billiards with parabolic
potential walls. The underlying classical periodic electron-hole orbits are
directly identified in terms of ``scar'' like features engraved in the quantum
wavefunctions of Andreev states determined here for the first time.
