PT-Symmetric Cubic Anharmonic Oscillator as a Physical Model

Details PT-Symmetric Cubic Anharmonic Oscillator as a Physical Model PT-Symmetric Cubic Anharmonic Oscillator as a Physical Model

2004-11-18

arxiv.org/abs/quant-ph/0411137v4

J.Phys.A38:6557-6570,2005; Erratum-ibid.A38:8185,2005

Physics

Quantum Physics

16 pages, 3 figures, Erratum to published version added

Scientific paper

10.1088/0305-4470/38/29/010

We 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=p^1/(2m)+\mu^2x^2/2+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.

Affiliated with

Also associated with

No associations

Rating

PT-Symmetric Cubic Anharmonic Oscillator as a Physical Model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with PT-Symmetric Cubic Anharmonic Oscillator as a Physical Model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and PT-Symmetric Cubic Anharmonic Oscillator as a Physical Model will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-258655