1 research outputs found
Analytic results for Gaussian wave packets in four model systems: II. Autocorrelation functions
The autocorrelation function, A(t), measures the overlap (in Hilbert space)
of a time-dependent quantum mechanical wave function, psi(x,t), with its
initial value, psi(x,0). It finds extensive use in the theoretical analysis and
experimental measurement of such phenomena as quantum wave packet revivals. We
evaluate explicit expressions for the autocorrelation function for
time-dependent Gaussian solutions of the Schrodinger equation corresponding to
the cases of a free particle, a particle undergoing uniform acceleration, a
particle in a harmonic oscillator potential, and a system corresponding to an
unstable equilibrium (the so-called `inverted' oscillator.) We emphasize the
importance of momentum-space methods where such calculations are often more
straightforwardly realized, as well as stressing their role in providing
complementary information to results obtained using position-space
wavefunctions.Comment: 18 pages, RevTeX, to appear in Found. Phys. Lett, Vol. 17, Dec. 200