  In this paper a quantum mechanical description of the assembly/disassembly
process for microtubules is proposed. We introduce creation and annihilation
operators that raise or lower the microtubule length by a tubulin layer.
Following that, the Hamiltonian and corresponding equations of motion are
derived that describe the dynamics of microtubules. These Heisenberg-type
equations are then transformed to semi-classical equations using the method of
coherent structures. The latter equations are very similar to the
phenomenological equations that describe dynamic instability of microtubules in
a tubulin solution.
