Spectroscopy of Heavy Mesons Expanded in $1/m_Q$

Operating just once with the naive Foldy-Wouthuysen-Tani transformation on the relativistic Fermi-Yang equation for $Q\bar q$ bound states described by the semi-relativistic Hamiltonian which includes Coulomb-like as well as confining scalar potentials, we have calculated heavy meson mass spectra of $D$ and $B$ together with higher spin states. Based on the formulation recently proposed, their masses and wave functions are expanded up to the second order in $1/m_Q$ with a heavy quark mass $m_Q$ and the lowest order equation is examined carefully to obtain a complete set of eigenfunctions for the Schr\"odinger equation. Heavy quark effective theory parameters, $\bar\Lambda$, $\lambda_1$, and $\lambda_2$, are also determined at the first and second order in $1/m_Q$.