Abstract: Harmonic oscillator is not only the most basic but also a representative problem in the quantum mechanics. The discussion on it in the coordinate representation by the Schrdinger equation is very complicated.The dimensionless ladder operators are introduced to calculate the eigenvalues and eigenvectors of Hamiltonian dexterously. The coherent states of harmonic oscillator is investigated by translation operators. It is found that the basic-vectors in the representation of coherent states are over-complete and there is the minimum uncertainty of position and its momentum in the coherent states.

Key words: harmonic oscillator, coherent states, ladder operator, translation operator