Coherent state of the harmonic oscillator

Abstract

In classical physics, for a harmonic oscillator with a certain energy, position and momentum oscillate in time sinusoidally. However, in a Quantum harmonic oscillator, the expectation of position and momentum operators at a given energy level (En) are both zero. So the two oscillators have different dynamics. However, under certain Quantum state, called Coherent state, the Quantum HO exhibits prominent classical behavior. The goal of my thesis is to find analytical solution of this state and discuss certain of its features.