  In this article we exploit the known commutative family in Y(gl(n)) - the
Bethe subalgebra - and its special limit to construct quantization of the
Gaudin integrable system. We give explicit expressions for quantum hamiltonians
QI_k(u), k=1,..., n. At small order k=1,...,3 they coincide with the
quasiclassic ones, even in the case k=4 we obtain quantum correction.
