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

Francisco M. Fernández, Javier Garcia

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.

http://arxiv.org/abs/1312.5117
Quantum Physics (quant-ph)