  In this note, we rederive quantum Pieri's formula and the rim hook algorithm
in quantum Schubert calculus by studying multiplication in the equivariant
cohomology ring of Grassmannians with respect to equivariant Schubert classes
which are characteristic classes. We also extend this idea in studying
equivariant quantum Schubert calculus, and obtain the equivariant quantum
Giambelli's and Pieri's formulae in terms of characteristic classes, with the
former formula shown to be free of quantum deformation.
