Final answer:
The parity of a 3D central potential, represented by Pψ = (-1)^lψ, reflects how the wavefunction ψ behaves under spatial inversion, which is determined by its angular momentum quantum number l.
Step-by-step explanation:
The statement regarding the parity of a 3-dimensional central potential states that Pψ = (-1)^lψ. This express the fact that the behavior of a wavefunction ψ under spatial inversion (parity transformation) is determined by the orbital angular momentum quantum number l.
In quantum mechanics, parity relates to the symmetry of the wavefunction when coordinates are inverted through the origin. For a central potential, which depends only on the distance from the origin and not the direction, the wavefunctions are often the solutions to the Schrödinger equation that include spherical harmonics. These spherical harmonics have defined parity, switching sign whenever l is odd and remaining the same when l is even. Therefore, applying the parity operator to a wavefunction yields a factor of (-1)^l, indicating the transformation properties of the wavefunction under inversion.
The dependence of this transformation on the orbital angular momentum reflects the underlying symmetry and spatial characteristics of these quantum states, and understanding this can provide insights into how physical systems behave under such transformations.