New perturbation theory for the nonstationary anharmonic oscillator

The new perturbation theory for the problem of the nonstationary anharmonic oscillator with polynomial nonstationary perturbation is proposed. As a zeroth-order approximation, the exact wavefunction of the harmonic oscillator with variable frequency in external field is used. Based on some intrinsic properties of unperturbed wavefunctions, the variational-iterational method is proposed, which makes it possible to correct both the amplitude and phase of the wavefunction. As an application, the first-order corrections are proposed for both the wavefunction and S-matrix elements for asymmetric perturbation potential of the type V(χ, τ)=α(τ)χ3+β(τ)χ4. The transition amplitude 'ground state-ground state' W00(λ:ρ) is analysed in detail depending on the perturbation parameter λ (including the strong coupling region λ∼1) and the one-dimensional refraction coefficient ρ. (author)