nLab phase

The term “phase” appears in different contexts:

• the complex phase of a complex number $c$ is the real number $\phi$ in the decomposition $c = {\vert c \vert} e^{i \phi}$;

• the phase of a wave function in physics is just this complex phase, the wave function being (locally) a function with values in the complex numbers;

• correspondingly then the phase difference between two linearly dependent vectors of a complex Hilbert space is the phase of the complex number that relates them;

• in thermodynamics and statistical physics different phases of a physical system label different order parameters that distinguish macroscopically different regions of the configuration space of the system;

• the phase space of a physical system is its space of classical solutions, typically given coordinates involving generalised momenta (for a relation of this to the phase of a wave function above see at phase and phase space in physics).