Abstract

This chapter describes the quantum mechanics of a harmonic oscillator, which is of essential importance in treating a phonon, using creation and annihilation operators. A number state, a coherent state, and a squeezed state are introduced. The number state is an eigenstate of the energy of the harmonic oscillator. The coherent state is a minimum uncertainty state. In the squeezed state, fluctuation of one of the conjugated variables is reduced and lowered than that of the vacuum state. Coherent and squeezed states are important in quantum optics and phononics. Time evolution of the mean value of position and variance for the harmonic oscillator is discussed.

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