Apart from a phase factor, Racah's W-coefficients are equal to Wigner's 6-j symbols, so any equation involving Racah's W-coefficients may be rewritten using 6-" j " symbols.
42.
Eigenmodes are useful in constructing a full solution to the wave equation, because each of them evolves in time trivially with the phase factor e ^ {-i \ omega t } . so that a full solution can be decomposed into an eigenmode expansion
43.
Media termed diattenuating ( or " dichroic " in the sense of polarization ), in which only the amplitudes of the two polarizations are affected differentially, may be described using a Hermitian matrix ( generally multiplied by a common phase factor ).
44.
This signifies that a particle which starts from the " n " th eigenstate remains in the " n " th eigenstate, simply picking up a phase factor \ scriptstyle { (-E _ nt / \ hbar ) }.
45.
Hilbert space "'P "'H, since two vectors that differ by a scalar factor ( or in physics terminology, two " kets " that differ by a " phase factor " ) correspond to the same physical quantum state.
46.
In quantum field theory, the analog to Noether's theorem, the Ward Takahashi identity, yields further conservation laws, such as the conservation of electric charge from the invariance with respect to a change in the phase factor of the gauge of the electric potential and vector potential.
47.
This expression actually means that when particle 1 and particle 2 are interchanged in a process where each of them makes a counterclockwise half-revolution about the other, the two-particle system returns to its original quantum wave function except multiplied by the complex unit-norm phase factor.
48.
This is often written as "'SU "'( 2 ) ?"'U "'( 1 ), ( which is strictly speaking only the same on the level of infinitessimal symmetries ) because the diagonal phase factor also acts on other fields in particular quarks.
49.
Since energy in quantum mechanics is defined as the phase factor exp (-iEt ) that one gets when one moves forward in time, the way to reverse time while preserving the sign of the energy is to also reverse the sense of " i ", so that the sense of phases is reversed.
50.
However some quantum physicists include a phase factor (-1 ) m in these definitions, which has the effect of relating the p x orbital to a " difference " of spherical harmonics and the p y orbital to the corresponding " sum " . ( For more detail, see Spherical harmonics # Conventions ).
