Considering a bound state which consists of one light anti-fermion  and one heavy quark (Q) in the so-called Cornell potential, we review a Hamiltonian formulation in which energy and wave functions of a bound state are expanded in 1/m_Q with m_Q a heavy quark mass.

We propose two different formulations in which the first non-trivial wave functions coincide with each other and accordingly the lowest energies (mass) are the same. The first non-trivial wave function can be, together with total angular momentum (j) and z component of angular momentum (j_z), classified in terms of the operator which is peculiar to the Hamiltonian with a potential depending only on an inter-quark distance. We also clarify the relation between  and the quantum number normally used in the heavy quark effective theory, total angular momentum of the light degrees of freedom,   with parity P.

We numerically calculate the spectra of heavy mesons, D, B and their higher spin states. Parameters in the heavy quark effective theory,  ,  λ₁, and λ₂, are also determined at the first and second order in I/m_Q. Developing also the formulation how to calculate the semileptonic weak form factors using the rest frame wave functions, we numerically calculate the dynamical I/m_Q corrections to those for the process   → D^(*)l v. The formula for the Isgur-Wise function slope is also given, the lower bound for a slope of the Isgur-Wise function at the origin is given by -1/2, and its numerical value is calculated to be -0.820.