  We consider a suspended elastic rod under longitudinal compression. The
compression can be used to adjust potential energy for transverse displacements
from harmonic to double well regime. As compressional strain is increased to
the buckling instability, the frequency of fundamental vibrational mode drops
continuously to zero (first buckling instability). As one tunes the separation
between ends of a rod, the system remains stable beyond the instability and
develops a double well potential for transverse motion. The two minima in
potential energy curve describe two possible buckled states at a particular
strain. From one buckled state it can go over to the other by thermal
fluctuations or quantum tunnelling. Using a continuum approach and transition
state theory (TST) one can calculate the rate of conversion from one state to
other. Saddle point for the change from one state to other is the straight rod
configuration. The rate, however, diverges at the second buckling instability.
At this point, the straight rod configuration, which was a saddle till then,
becomes hill top and two new saddles are generated. The new saddles have bent
configurations and as rod goes through further instabilities, they remain
stable and the rate calculated according to harmonic approximation around
saddle point remains finite. In our earlier paper classical rate calculation
including friction has been carried out [J. Comput. Theor. Nanosci. {\bf 4}
(2007) {\it 1}], by assuming that each segment of the rod is coupled to its own
collection of harmonic oscillators - our rate expression is well behaved
through the second buckling instability. In this paper we have extended our
method to calculate quantum rate using the same system plus reservoir model. We
find that friction lowers the rate of conversion.
