Symmetry Principles and Conservation Laws in Atomic and ...

GENERAL ARTICLE1.3 CPT SymmetryThe `Time Reversal Symmetry' (T) is another discretesymmetry. This has a characteristically di®erent formin quantum mechanics that has no classical analogue.The name time-reversal is perhaps inappropriate, becauseit would make a layman suspect that it is merelythe inverse of the `time evolution', which is not thecase. In quantum theory, the operator for `time evolution'is unitary, but that for time-reversal is antiunitary.The quantum mechanical operator ¦ for parity anticommuteswith the position and the momentum operator,but commutes with the operator for angular momentum.On the other hand, the operator for time-reversal,£ commutes with the position operator, but anticommuteswith both the linear and the angular momentumoperators.In quantum theory,the operator for‘time evolution’ isunitary, but that fortime-reversal isantiunitary.An important consequence of these properties is thefact that the response of a wavefunction to time-reversalwould include not merely t going to ¡t in the argumentof the wavefunction, but also simultaneous complex conjugationof the wavefunction. This property connectsthe quantum mechanical solutions of an electron{ioncollision problem with those of electron{atom scatteringthrough time-reversal symmetry. The physical contentof this connection is depicted in Figure 3 which representsthe fact that in a photoionization experiment it isthe escape channel for the photoelectron which is uniquewhereas in an electron{ion scattering experiment it isthe entrance channel of the projectile electron which is(a)(b)Figure 3. Schematic diagramshowing the time-reversalrelation betweenphotoionization and scatteringprocesses in atomicphysics.RESONANCE October 2010933