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H. Jensen, Phys. Rev. A. 45, 2686 (1992). [16] D. Bohm, Phys. Rev. 85, 166 (1952); 85, 180 (1952); Nature, 315, 294 0985). [17] I follow here J. J. Sakurai's argument. See his quantum text book, Modern Quantum Mechanics (Benjamin Cummings, Menlo Park, CA, 1985). [18] For a comprehensive argument example, D. H. W. about taking a classical limit, see for Science, 253, 626 (1991) Noid, M. L. Koszykowski, R. A. Marcus, Annu. Rev. Phys. Chem. 32, 267 (1981); W. P. Reinhardt, Chaotic Behaviors in Quantum Systems: Theory and Applications, edited by G.
16] D. Bohm, Phys. Rev. 85, 166 (1952); 85, 180 (1952); Nature, 315, 294 0985). [17] I follow here J. J. Sakurai's argument. See his quantum text book, Modern Quantum Mechanics (Benjamin Cummings, Menlo Park, CA, 1985). [18] For a comprehensive argument example, D. H. W. about taking a classical limit, see for Science, 253, 626 (1991) Noid, M. L. Koszykowski, R. A. Marcus, Annu. Rev. Phys. Chem. 32, 267 (1981); W. P. Reinhardt, Chaotic Behaviors in Quantum Systems: Theory and Applications, edited by G.
Now we use (2-19) to solve 1//first, then we find the required solution _/'. The SchriSdinger equation (2-19) is formally solved to give 24 _(q, t) = exp( - i H _n(t') dt' ) _(q, 0). _0 _ (2-21) A A A A Then the split operatoralgorithm[8,9] splitsH _n into T (p), V (q), and results in a discrete form with a time-ordering operator 0 as W(q,t+At) = 0 exp [ - i ^ I t+At H(t ') dt" ] _q,t), .... =_ _, q,t; tOv,(q,t) + ,_{(atP}, (2-22) A where U = exp{ - (_/2) tit' exp{ - i = exp{- i (V ) dt"exp{ - i + P--_s_ t')2]dt'} exp{- i (0 ina_ x expl - = exp{- V (q) dt'} exp{ - i (T /2) dt' p(l-cosq) dt'} + _-_Y CO into t ') 21dtq, ] dt'} exp{ - i = "F(p,t) Y(q)T(p,t)- A (2-23) ] dt'}, _'eff 'Yell Tell.