Comparison of two semiclassical expansions for a family of PT-symmetric oscillators

2013/12/18 by Francisco M. Fernández, Fernández, Francisco M., Javier Garcia +1
Physics and Astronomy · #Gyrotron and Vacuum Electronics Research #Neutrino Physics Research #Quantum Mechanics and Non-Hermitian Physics #quant-ph

paper · pdf · doi:10.48550/arxiv.1312.5117

arxiv created 2013/12/18 · arxiv updated 2013/12/19

Abstract

We show that a recently developed semiclassical expansion for the eigenvalues of PT-symmetric oscillators of the form V(x)=(ix)^2N+1+bix does not agree with an earlier WKB expression for V(x)=-(ix)^2N+1 the case b=0. The reason is due to the choice of different paths in the complex plane for the calculation of the WKB integrals. We compare the Stokes and anti-Stokes lines that apply to each case for the quintic oscillator and derive a general WKB expression that contains the two earlier ones.

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