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.
Quantum Physics (quant-ph)

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