phase factor

This phase factor is itself a complex number of absolute value 1.

In comparison to the former expression, only a phase factor with unit length occurs.

This phase factor here is called the mutual statistics.

The phase factor is represented by a plane wave.

Note, however, that the direction of the shift is modified by the exponential phase factor.

Under this transformation the basis states obtain the same phase factor .

The new phase factor can be canceled out by an appropriate choice of gauge for the eigenfunctions.

In optics, the phase factor is an important quantity in the treatment of interference.

A phase factor, β is introduced, which accounts for the thickness of each layer.

Indeed, the phase factor, varying with t, disappears naturally.

An odd permutation of the columns gives a phase factor:

The sum of the phase factors is a simple geometric series and the structure factor becomes:

When acting on an eigenket, the phase factor appears in each term of the resulting state, which makes it physically irrelevant.

This transformation introduces a phase factor that is normally ignored as non-physical, but has application in some problems.

The wavefunction itself is not stationary: It continually changes its overall complex phase factor, so as to form a standing wave.

In general the transition dipole moment is a complex vector quantity that includes the phase factors associated with the two states.

In other words, there is no physical difference between two polarization states and , between which only a phase factor differs.

We have explicitly extracted the exponential phase factors exp( iE't/) on the right hand side.

If two unit vectors differ only by a scalar of magnitude 1, known as a "global phase factor," then they are indistinguishable.

Therefore, if we know the particle's motion, cross products term, and phase factor, we could calculate the radiation integral.

The origin of the different signs for capacitive and inductive reactance is the phase factor in the impedance.

The translational symmetry of the crystal implies the wave function under translation can change only by a phase factor:

Thus we see that the eigenstates of the Hamiltonian are stationary states: they only pick up an overall phase factor as they evolve with time.

On the basis of this distinction, it also clear that the modulation by the phase factors in the probability expression of Eq.

Therefore, the exact information of the phase factor () is unknown to the observer; for this, an interference experiment is required.