  The microscopic quantum interference associated with excitonic condensation
in Ta$_2$NiSe$_5$ is studied in the BCS-type mean-field approximation. We show
that in ultrasonic attenuation the coherence peak appears just below the
transition temperature $T_{\rm c}$ whereas in NMR spin-lattice relaxation the
rate rapidly decreases below $T_{\rm c}$; these observations can offer a
crucial experimental test for the validity of the excitonic condensation
scenario in Ta$_2$NiSe$_5$. We also show that the excitonic condensation
manifests itself in a jump of the heat capacity at $T_{\rm c}$ as well as in
softening of the elastic shear constant, in accordance with the second-order
phase transition observed in Ta$_2$NiSe$_5$.
