Intrinsic parity
Encyclopedia
In quantum mechanics
, the intrinsic parity
is a phase factor
that arises as an eigenvalue of the parity operation (a reflection about the origin). To see that the parity's eigenvalues are phase factors, we assume an eigenstate of the parity operation (this is realized because the intrinsic parity is a property of a particle
species) and use the fact that two parity transformations leave the particle in the same state, thus the new wave function can differ by only a phase factor, i.e.:
thus 
, since these are the only eigenstates satisfying the above equation.
The intrinsic parity's phase is conserved for non-weak interactions (the product of the intrinsic parities is the same before and after the reaction), since [P,H]=0, i.e.: the Hamiltonian
is invariant under a parity transformation. The intrinsic parity of a system is the product of the intrinsic parities of the particles, for instance for noninteracting particles we have
. Since the parity commutes with the Hamiltonian, its eigenvalue does not change with time, therefore the intrinsic parity's phase is a conserved quantity.
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...
, the intrinsic parity
Parity (physics)
In physics, a parity transformation is the flip in the sign of one spatial coordinate. In three dimensions, it is also commonly described by the simultaneous flip in the sign of all three spatial coordinates:...
is a phase factor
Phase factor
For any complex number written in polar form , the phase factor is the exponential part, i.e. eiθ. As such, the term "phase factor" is similar to the term phasor, although the former term is more common in quantum mechanics. This phase factor is itself a complex number of absolute value 1...
that arises as an eigenvalue of the parity operation (a reflection about the origin). To see that the parity's eigenvalues are phase factors, we assume an eigenstate of the parity operation (this is realized because the intrinsic parity is a property of a particle
Subatomic particle
In physics or chemistry, subatomic particles are the smaller particles composing nucleons and atoms. There are two types of subatomic particles: elementary particles, which are not made of other particles, and composite particles...
species) and use the fact that two parity transformations leave the particle in the same state, thus the new wave function can differ by only a phase factor, i.e.:
thus , since these are the only eigenstates satisfying the above equation.The intrinsic parity's phase is conserved for non-weak interactions (the product of the intrinsic parities is the same before and after the reaction), since [P,H]=0, i.e.: the Hamiltonian
Hamiltonian (quantum mechanics)
In quantum mechanics, the Hamiltonian H, also Ȟ or Ĥ, is the operator corresponding to the total energy of the system. Its spectrum is the set of possible outcomes when one measures the total energy of a system...
is invariant under a parity transformation. The intrinsic parity of a system is the product of the intrinsic parities of the particles, for instance for noninteracting particles we have
. Since the parity commutes with the Hamiltonian, its eigenvalue does not change with time, therefore the intrinsic parity's phase is a conserved quantity.