Phase factor
For any complex number written in Complex number#Polar [complex plane|polar form], the phase factor is the complex exponential, where the variable is the phase of a wave or other periodic function. The phase factor is a unit complex number, i.e. a complex number of absolute value 1. It is commonly used in quantum mechanics and optics. It is a special case of phasors, which may have arbitrary magnitude.
Multiplying the equation of a plane wave by a phase factor shifts the phase of the wave by :
In quantum mechanics, a phase factor is a complex coefficient that multiplies a ket or bra. It does not, in itself, have any physical meaning, since the introduction of a phase factor does not change the expectation values of a Hermitian operator. That is, the values of and, where, are the same. However, differences in phase factors between two interacting quantum states can sometimes be measurable and this can have important consequences.
In optics, the phase factor is an important quantity in the treatment of interference.