  We show that the uncertainty principle product for the position and momentum
operators for a system described by the Hamiltonian $ \hat H=
\frac{\hat{p}^2}{2m} +\frac{1}{2} m \omega^2 \hat{x}^2+\frac{\mu}{2}(\hat x
\hat p+ \hat p \hat x)$ where $\mu<\omega$ reads $\Delta x \Delta
p\ge\frac{\hbar \omega}{2\sqrt{\omega^2-\mu^2}}$. All the values bellow this
lower bound are thus quantum-mechanically forbidden. We construct the
annihilation and creation operators for this system and we calculate the
expectation values of the operators $\hat p$ and $\hat x$ with respect to the
corresponding coherent states.
