Av. Bogdanov et As. Gevorkyan, NEW PERTURBATION-THEORY FOR THE NONSTATIONARY ANHARMONIC-OSCILLATOR, Journal of physics. A, mathematical and general, 30(21), 1997, pp. 7413-7425
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.