  We consider a harmonic oscillator (HO) with a time dependent frequency which
undergoes two successive abrupt changes. By assumption, the HO starts in its
fundamental state with frequency \omega_{0}, then, at t = 0, its frequency
suddenly increases to \omega_{1} and, after a finite time interval \tau, it
comes back to its original value \omega_{0}. Contrary to what one could naively
think, this problem is a quite non-trivial one. Using algebraic methods we
obtain its exact analytical solution and show that at any time t > 0 the HO is
in a squeezed state. We compute explicitly the corresponding squeezing
parameter (SP) relative to the initial state at an arbitrary instant and show
that, surprisingly, it exhibits oscillations after the first frequency jump
(from \omega_{0} to \omega_{1}), remaining constant after the second jump (from
\omega_{1} back to \omega_{0}). We also compute the time evolution of the
variance of a quadrature. Last, but not least, we calculate the vacuum
(fundamental state) persistence probability amplitude of the HO, as well as its
transition probability amplitude for any excited state.
