## Abstract

The symmetry and dynamics of the full solution of anharmonic oscillator with λ q^{4} type anharmonicity and unit oscillator frequency is studied numerically for intermediate values of λ using the Wigner function formalism. The calculations show that for any λ > 0 the ground state of the system quickly develops non-perturbative quantum fluctuations and beyond λ ∼ 0.5 any effective mean field assumption using correlated Gaussians is expected to fail. We briefly discuss the validity of the mean field solution below λ = 0.5 and compare with the numerical results. We further examine the marginal phase probability distribution corresponding to that of the exact phase operator. The marginal phase probability distrubution proves to be a valuable tool to extract the properties of the phase operator and it has potential use in building the necessary intuititive ground for the quantum action-angle formalism of the non-integrable quantum systems.

Original language | English |
---|---|

Pages (from-to) | 393-398 |

Number of pages | 6 |

Journal | Turkish Journal of Physics |

Volume | 21 |

Issue number | 3 |

Publication status | Published - 1997 |

Externally published | Yes |