Wave functions of log-periodic oscillators

We use the Lewis and Riesenfeld invariant method [J. Math. Phys. 10, 1458 (1969)] and a unitary transformation to obtain the exact Schrodinger wave functions for time-dependent harmonic oscillators exhibiting log-periodic-type behavior. For each oscillator we calculate the quantum fluctuations in the coordinate and momentum as well as the quantum correlations between the coordinate and momentum. We observe that the oscillator with m = m(0)t/t(0) and omega = omega(0)t(0)/t, which exhibits an exact log-periodic oscillation, behaves as the harmonic oscillator with m and omega constant. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3601739]