Linear Harmonic Oscillator: I Solution of the Schrödinger Equation and Relationship with the Classical Oscillator

The linear harmonic oscillator problem is one of the most fascinating problems in quantum mechanics. It allows us to understand the basic features of a quantum system along with its transition to the classical domain. It has applications in many problems in physics; e.g. in studying the vibrational spectra of molecules, quantum theory of radiation, etc. In this chapter, we will first obtain solutions of the onedimensional Schrodinger equation corresponding to the linear harmonic oscillator and then discuss the time evolution of the coherent states of the oscillator which represent the quantum mechanical analogs of the classical oscillator.