TAPPERT: SELECTED APPLICATIONS OF THE PARABOLIC- EQUATION METHOD IN 

 UNDERWATER ACOUSTICS 



No- al modes; 



, 92(j; k / c2 



-^ J^ + —\^^— - ll "l^ = k^ (27) 



2k 9z2 2 \c^(z) / ^n n^n 



ii{z,r) = y* a (r) (jj (z) e^ n^ 

 ^ ^-' n n 



n 



Density matrix: 



Coupling coefficients: 



k r 



V (r) = — / dz i>*{z) 6c(z,r) ij; (z) 

 nm c ^ n m 



Transition probability: 



Master equation: 



Figure 23. PAULI MASTER EQUATION PROCEDURE 



189 



(28) 



p (r) = <a (r) a* (r)> (29) 



*^nm ^ n m ^ 



(30) 



Y = 2tt < Iy (k - k ) |2> (31) 



'nm ' nm n m ' 



— p =Ey (P -P) (32) 



3r nn m nm mm nn 



