Department of Mathematics2024-11-0920050305-447010.1088/0305-4470/38/29/0102-s2.0-22544485701http://dx.doi.org/10.1088/0305-4470/38/29/010https://hdl.handle.net/20.500.14288/7043We perform a perturbative calculation of the physical observables, in particular, pseudo-Hermitian position and momentum operators, the equivalent Hermitian Hamiltonian operator and the classical Hamiltonian for the PT-symmetric cubic anharmonic oscillator, H = -1/2m p(2) + 1/2 mu(2) x(2) + i epsilon x(3). Ignoring terms of order epsilon(4) and higher, we show that this system describes an ordinary quartic anharmonic oscillator with a position-dependent mass, and real and positive coupling constants. This observation elucidates the classical origin of the reality and positivity of the energy spectrum. We also discuss the quantum-classical correspondence for this PT-symmetric system, compute the associated conserved probability density and comment on the issue of factor ordering in the pseudo-Hermitian canonical quantization of the underlying classical system.PhysicsMathematical physicsJournal Article231160100014Q25498