ANDREEV BOUND STATES. SOME QUASICLASSICAL REFLECTIONS
Lin Y., Leggett A.J.

Received: June 18, 2014

DOI: 10.7868/S0044451014120049

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We discuss a very simple and essentially exactly solvable model problem which illustrates some nice features of Andreev bound states, namely, the trapping of a single Bogoliubov quasiparticle in a neutral s-wave BCS superfluid by a wide and shallow Zeeman trap. In the quasiclassical limit, the ground state is a doublet with a splitting which is proportional to the exponentially small amplitude for ``normal'' reflection by the edges of the trap. We comment briefly on a prima facie paradox concerning the continuity equation and conjecture a resolution to it. Contribution for the JETP special issue in honor of A. F. Andreev's 75th birthday}