  In this paper we consider linear, time dependent Schr\"odinger equations of
the form $i \partial_t \psi = K_0 \psi + V(t) \psi $, where $K_0$ is a positive
self-adjoint operator with discrete spectrum and whose spectral gaps are
asymptotically constant.
  We give a strategy to construct bounded perturbations $V(t)$ such that the
Hamiltonian $K_0 + V(t)$ generates unbounded orbits. We apply our abstract
construction to three cases: (i) the Harmonic oscillator on $\mathbb R$, (ii)
the half-wave equation on $\mathbb T$ and (iii) the Dirac-Schr\"odinger
equation on the sphere. In each case, $V(t)$ is a smooth and periodic in time
pseudodifferential operator and the Schr\"odinger equation has solutions
fulfilling $\| \psi(t) \|_r \gtrsim |t|^{r }$ as $|t| \gg 1$.
