  We study differential and integral relations for the quantum Jost solutions
associated with an integrable derivative nonlinear Schrodinger (DNLS) model. By
using commutation relations between such Jost solutions and the basic field
operators of DNLS model, we explicitly construct first few quantum conserved
quantities of this system including its Hamiltonian. It turns out that this
quantum Hamiltonian has a new kind of coupling constant which is quite
different from the classical one. This modified coupling constant plays a
crucial role in our comparison between the results of algebraic and coordinate
Bethe ansatz for the case of DNLS model. We also find out the range of modified
coupling constant for which the quantum $N$-soliton state of DNLS model has a
positive binding energy.
