Optional Problems on the Harmonic Oscillator

â φα = αφα , with α a complex number (see next page for a discussion of â and â†). Such a state is called a “coherent state”. Coherent states turn out to be the closest quantum analog of classical states with well-defined amplitudes and phases, and are extremely important in e.g. the quantum mechanical description of laser light, radio cavities, Bose-Einstein condensates, and just about everything else that’s both macroscopic and quantum.