Quasiclassical trajectory-coherent states of an anharmonic oscillator

Based on the complex WKB—Maslov method, asymptotic solutions accurate within O(h²) are constructed for a class of wave packets — quasiclassical trajectory-coherent states for a quantum anharmonic oscillator with a potential V(x)=x²+x⁴. We obtain the behavior of the packet width and the deviations of the approximate solution as a function of time. The actual parameter of the quasiclassical expansion is shown to be h^1/2. We find the regions of variation of the potential parameters and of the initial data for which is small, while the breakdown time of the given accuracy and the packet spreading time are comparable to the time of a single particle revolution.Moscow Institute of Electric Machine Construction. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 21–27, September, 1993.