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Download Light and Matter Ic / Licht und Materie Ic by H. Haken (auth.), L. Genzel (eds.) PDF

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By H. Haken (auth.), L. Genzel (eds.)

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4. ;; ~~ ~~ ~ ~~. 0 "'~· 0 ~a "' ~~ 01- 11 -02,12- ;-- zz r-- t- r--- 9 " :.... - rr- ..... l 2 - 2 Fig. 16. Diffraction losses for confocal and plane-parallel resonator. e. 11 on p. 19. 4. g. by unequal apertures or curvatures, one must require that the field pattern is reproduced (besides a constant factor) after a full round trip from 51 to 5 2 back to 51 • One then has to apply Huygen's principle twice. 2) K(x, x'; y, y') J = dx" dy" exp (i ~ [x" (x + x') +y" (y +y')]). 2} This kernel depends on the shape and size of the reflectorS, and has been evaluated by BoYD and KoGELNIK for various situations.

3. 9) becomes db+ ~ " =iw0 b+-xb+ +i~g! Bt (t0) . F+(t) where the last term is evidently the fluctuating force. 15) Q) iiw is the occupation number of the mode corresponding to frequency w of the heatbath. 15) can be directly expressed by the damping constant x only for the temperature T=O. 18) w and (F(t) F+(t')) w always appear under an integral which contains a factor eiw,t, where w 0 is the frequency of the harmonic oscillator (light field). ,,(T) + 1 )~ (t- t'). 19) expresses the fact that the heatbath has a very short memory.

0 for parity reasons (az+~)~ = -iv12 (at~),. ,,. bt ((ata 2 ) , . ). ,,. ,,. this equation is the hermitian conjugate of Eq. (III. 12). 14) AN=ata 2 -at~. ,p bt (afa 2 ),. ,,. b;. 15) ). (ata 2)~ =i vlll(ata2 ),. ,,. b;. AN,.. 16) ). Because the third equation is merely the hermitian conjugate of Eq. 16), we drop it. 6. The formal equivalence of the system of atoms each having 2 levels with a system of t spins 1 • Because the spins as well as the electrons belonging to different atoms can be considered as distinguishable, it is sufficient to prove the equivalence for a single spin and a single electron.

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