NEW PERTURBATION-THEORY FOR THE NONSTATIONARY ANHARMONIC-OSCILLATOR

The new perturbation theory for the problem of the nonstationary anhar monic oscillator with polynomial nonstationary perturbation is propose d. As a zeroth-order approximation, the exact wavefunction of the harm onic oscillator with variable frequency in external field is used. Bas ed on some intrinsic properties of unperturbed wavefunctions, the vari ational-iterational method is proposed, which makes it possible to cor rect both the amplitude and phase of the wavefunction. As an applicati on, the first-order corrections are proposed for both the wavefunction and S-matrix elements for asymmetric perturbation potential of the ty pe V (x, tau) = alpha(tau)x(3) + beta(tau)x(4). The transition amplitu de 'ground state-ground state' W-00(lambda; rho) is analysed in detail depending on the perturbation parameter lambda (including the strong coupling region lambda similar to 1) and the one-dimensional refractio n coefficient rho.