4 - Physical properties

Summary

Classical and quantum properties

We shall use the term physical property to refer to something which can be said to be either true or false for a particular physical system. Thus “the energy is between 10 and 12 μJ” or “the particle is between x₁ and x₂” are examples of physical properties. One must distinguish between a physical property and a physical variable, such as the position or energy or momentum of a particle. A physical variable can take on different numerical values, depending upon the state of the system, whereas a physical property is either a true or a false description of a particular physical system at a particular time. A physical variable taking on a particular value, or lying in some range of values, is an example of a physical property.

In the case of a classical mechanical system, a physical property is always associated with some subset of points in its phase space. Consider, for example, a harmonic oscillator whose phase space is the x, p plane shown in Fig. 2.1 on page 12. The property that its energy is equal to some value E₀ > 0 is associated with a set of points on an ellipse centered at the origin. The property that the energy is less than E₀ is associated with the set of points inside this ellipse. The property that the position x lies between x₁ and x₂ corresponds to the set of points inside a vertical band shown cross-hatched in this figure, and so forth.