IMPROVEMENTS ON THE PERTURBED HARMONIC OSCILLATOR LADDER OPERATORS METHOD IN THE NON LINEAR QUANTUM FIELD THEORY AND THE LASER THEORY
Fubin Li, 淮北煤炭师范学院物理系,安徽
The interaction potential with the form as V(x)= x2+λx2/(1+gx2) where g >0, appears in several areas of laser theory, quantum field theory, atom and nuclear physics. One could consider that the solution of the eigenequation either by the classical Rayleigh-Schr?dinger perturbation scheme or by the perturbed ladder operators scheme. Nevertheless, the perturbation series does not converge for any values of λ and g. In the present paper, it is shown that this difficulty can be overcome as long as the potential function can be expanded in a convergent series on the basis ofthe Hermite polynomials. Therefore, the eigenequation ((d2)/(dx2)-V(x)+ξ)φ(x)=0,∞2)/(dX2)-b2X2-Σkc2kH2k(b1/2X)+ξ)φ(X)=0.
Acta Physica Sinica•Jan 1, 1989•1 citation