A Phase Space Investigation of the Quartic Oscillator Ground State

Authors: T. HAKİOĞLU

Abstract: The symmetry and dynamics of the full solution of anharmonic oscillator with \lambda\, q^4 type anharmonicity and unit oscillator frequency is studied numerically for intermediate values of \lambda using the Wigner function formalism. The calculations show that for any \lambda > 0 the ground state of the system quickly develops non-perturbative quantum fluctuations and beyond \lambda \sim 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 \lambda = 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.