Classical and quantum oscillators of quartic anharmonicities: second-ordersolution

An analytical solution up to the second order in the coupling constant lamb da is obtained for a classical quartic anharmonic oscillator by using Taylo r series method. Our solution yields, as a special instance, the correspond ing results obtained by using Laplace transform. With the help of correspon dence principle, the classical solution is used to obtain the solution corr esponding to a quantum quartic anharmonic oscillator. In the weak coupling regime (i.e., anharmonic constant lambda much less than 1), the so-called s ecular terms in classical and quantum solutions are tucked in (summed up) t o avoid the nonconvergence. Both the classical and quantum solutions are us ed to obtain the frequency shifts of the quartic oscillators. It is found t hat these frequency shifts coincide exactly with those of the earlier resul ts obtained by other methods. From the quantum field theoretic point of vie w, our solution exhibits the so-called Lamb shift. As an application of the solution for the quantum oscillator, we examine the possibility of getting squeezed states out of the input coherent light interacting with a nonline ar medium of inversion symmetry. (C) 2001 Elsevier Science B.V. All rights reserved.