The coherent state evolves in time and space differently than both the thermal and Fock states. The most compact way to visualize a coherent state is using the Wigner function as in Figure .

**Figure:** The Wigner function for a Coherent state for

The average momentum and position of the field oscillate sinusoidally, while the variance possesses a constant value of one half which is represented by a small circle of uncertainty moving around a larger circle. This same information can be observed in a plot of the **q**, and **p**, plotted versus time, as in Figure .

**Figure:** **q**, vs **t** and **p**, vs **t** for a Coherent state with .

Notice that Figure is quite wavelike; indeed, as the of the coherent state is increased the variance remains constant, but the amplitude of the curve increases. Therefore, as increases, a coherent state behaves more and more like a classical electromagnetic wave. A laser is a source of coherent radiation; therefore, BlochApp can be thought of quantum mechanically as a two--state atom interacting with a coherent electromagnetic field. Plot the E and B for a coherent state. What kind of wavelike character does it have? Compare this result with that for a thermal state. Plot coherent states with larger values of as well.

Wed May 17 14:34:24 EDT 1995