Anharmonic oscillator systems

Gaussian Basis Sets for Model Anharmonic Oscillator Systems

Coupling Constant Analyticity for the Anharmonic Oscillator*

We study the analytic properties of the singular perturbation theory forp2 + x2 + gx*. We prove rigorously several of the properties of the energy levels, previously found by C. Bender and T. T. Wu using methods of unknown validity. In particular: (a) En@) has a “global” third-order branch point at /3 = 0, i.e., any path of continuation which winds three times around /I = 0 and circles clockwis...

Wigner function for a driven anharmonic oscillator

We consider the quantum model of a driven anharmonic oscillator, in the presence of dissipation, and present an exact analytic solution for the corresponding Wigner function in the steady-state regime. This provides explicit phase-space images of the resulting state of the cavity mode, and allows us to understand how the quantum interference is built up into it. The photon number probability di...

Quantum anharmonic oscillator and its statistical properties

The simple quantum harmonic oscillator is an excellent model of many physical systems, e.g. electromagnetic field. The excitation particles or quanta of the electromagnetic field are called photons [1, 2] Moreover it applies for systems of atoms (ions, nuclei) in ideal crystals interacting via harmonic attractive force, etc. In the latter case the elementary excitation particles of vibrations o...

Dispersive hyperasymptotics and the anharmonic oscillator

Hyperasymptotic summation of steepest-descent asymptotic expansions of integrals is extended to functions that satisfy a dispersion relation. We apply the method to energy eigenvalues of the anharmonic oscillator, for which there is no known integral representation, but for which there is a dispersion relation. Hyperasymptotic summation exploits the rich analytic structure underlying the asympt...