Quantum and classical analyses of Hamiltonian constructed from Casimir operators of Lie algebras (Lie代数のCasimir演算子によって構成されるハミルトニアンの量子・古典解析) The algebraic method for molecules is known as a technique to formulate and to solve a model of molecular vibration. This method enables us to construct a so-called algebraic Hamiltonian from a Lie algebra and to calculate its spectrum, which can be compared with experimentally measured spectrum. Up to the present, it has been known that an algebraic Hamiltonian based on the su(2) algebra contains the Morse oscillator. But the contents of systems based on more general algebras like su(3) and su(4) are not yet uncovered. In this master thesis, properties of the dynamical systems based on su(2), su(3) and su(4) are examined from both the viewpoint of quantum and classical mechanics. Since the algebraic Hamiltonian has some symmetry by its definition, separation of variables is applicable in the context of quantum mechanics. On the other hand, in the context of classical mechanics, the Marsden-Weinstein method, which reduces the degrees of freedom of dynamical system with symmetry, is applicable. As the result, in both contexts, it is shown that the Morse oscillator is induced from the original algebraic systems. It is also shown that the Morse oscillators induced from the algebraic systems have different inner product structure for probability interpretation or different metric structure from the ordinary Morse oscillator.