By S. Bashir
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By means of relations Hˆ 1 Tlm Hˆ 1*ml and Hˆ 2Tlm Hˆ 2*ml , we get the time reversal of transition amplitude for the second order processes according to(11) t t 1 1 i t 2 1 al t Hˆ 2Tlm e lm dt Hˆ 1 Tlk ak t e ilk t dt i 0 i k 0 t t 1 ˆ * iml t 1 1 H 2 ml e dt Hˆ 1*kl ak t e ikl t dt i 0 i k 0 (40) Let Hˆ 2*ml Fˆ2ml e i 2 t Fˆ2ml e i 2 t Fˆ0ml , when m l , we have m l 0 and iq 2 E02 i 2 k R 0 Fˆ2ml e m r l c * iq 2 E02 i 2 k R 0 Fˆ2ml e m r l c * Fˆ0ml 0 (41) So the time reversal of transition probability amplitude of the second process is 2 aTm t al 2 t k i 2 mk kl t i kl t ˆ Fˆ1mk F1kl e 1 e 1 kl 2 mk 2 mk kl k k k i 2 ml t i 2 ml t Fˆ2ml e 1 Fˆ2ml e 1 2 ml 2 ml i t i kl t ˆ Fˆ1mk F1kl e mk kl 1 e 1 2 mk mk kl kl i t i kl t Fˆ1mk Fˆ1kl e mk kl 1 e 1 2 kl mk mk kl i 2 mk kl t i kl t Fˆ1mk Fˆ1kl e 1 e 1 2 kl mk 2 mk kl (42) 30 Electromagnetic Radiation When ml , we take k m in the third and fifth items of the formula.
At last, the influences of symmetry violation of time reversal on the foundation theory of laser and non-equilibrium statistical physics are discussed. The phenomena of producing laser without the reversion of particle population and transition without radiation can be well explained. The result indicates that the irreversibility of evolution processes of macrosystems originates from the irreversibility of micro-processes. The irreversibility paradox can be eliminated thoroughly. By introducing retarded electromagnetic interaction, the forces between classical changed particles are not conservative ones.
The formula represents the probability amplitude of an electron transiting from the initial state l into the final state m . , only the first item is considered when ml and the second one is considered when ml in (13). But up to now we have not decided which one is the state of high-energy level and which one is the state of low-energy level. In fact, electron can either transit into higher-energy state m from low-energy state l by absorbing a photon, Retarded Electromagnetic Interaction and Symmetry Violation of Time Reversal in High Order Stimulated Radiation and Absorption Processes of Lights as Well as Nonlinear Optics ...