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Extra info for Computation of atomic processes : a handbook for the ATOM programs
This is, in fact, the basis for assigning a definite parity to stationary atomic states. It came as a shock to the physics community when in the late 1950s and 1960s, parity (P) violation and then also CP violation were experimentally discovered. In fact, remarkably, all discrete symmetries have now been experimentally shown to be violated, with the sole exception of the combination of all three symmetries, CPT. This symmetry is currently being checked by more and more precise experiments. Atomic and molecular experiments are at the forefront of experimental studies of discretesymmetry violations; however, the manifestations of these violations in atomic and molecular systems typically appear as quite small effects that can usually be neglected, except in the specific context of the study of discrete-symmetry violations.
For each step, the rotation direction is indicated by a curved arrow; the initial position of the body is shown as a cubic frame, and the final position is shown as a filled cube. 35 z ′′ y y ′ β z α γ x x y y Rather than attempting to write out the matrix for rotation about an arbitrary axis, we can decompose an arbitrary rotation into a series of rotations about the Cartesian axes. An arbitrary rotation can be described by three successive rotations by the Euler angles α, β, and γ. To describe these rotations in the active sense, we make use of body-fixed axes, which undergo the same active rotation as the rotating object, so as to remain fixed with respect to it, as opposed to the original set of space-fixed axes, which do not change during an active rotation.
From this argument, we see that the density of the probability to find an electron at a certain point in space, being proportional to the modulus squared of the wave function, should not change under spatial inversion. Wave functions that remain unchanged under spatial inversion are said to be of positive or even parity. Wave functions that change sign under spatial inversion are said to be of negative or odd parity. Looking at the decomposition of Eq. 5), it is clear that under coordinate-system inversion, the radial part of the wave function Rnl (r) remains unchanged, because inversion does not change the modulus of the radius vector r.