  Resonance (quasinormal) states correspond to non-Hermitian solutions to the
Schr\"odinger equation obeying outgoing boundary conditions which lead to
complex energy eigenvalues and momenta. Following the normalization rule for
resonance states obtained from the residue at a complex pole of the outgoing
Green's function to the problem, we propose a definition of expectation value
for these states and use it to investigate the extent of validity of the
Heisenberg uncertainty relations for potentials that vanish after a distance.
We derive analytical expressions for the expectation values involving the
momentum and the position for a given resonance state and find in model
calculations that the Heisenberg uncertainty relations are satisfied for a
broad range of potential parameters. A comparison of our approach with that
based on the regularization method by Zel'dovich yields very similar results
except for resonance energies very close to the energy threshold. Our work
shows that the validity of the Heisenberg uncertainty relations may be extended
to the non-Hermitian resonance state solutions to the Schr\"odinger equation.
