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V. Fedotov and I. Hofmann, Phys. Rev. ST-AB 5,024202 (2002). 15. T. Wangler, R F Linear Accelerators (Wiley, New York, 1998). 16. L. D. Landau and E. M. Lifshitz, Physical Kinetics (Butterworth-Heinemann, Oxford, 1996). 17. F. Ruggiero, Ann. Phys. ) 153,122 (1984); F. Ruggiero, E. Picasso and L. A. Radicati, Ann. Phys. (N. ) 197,396 (1990). 18. J. Struckmeier, Phys. Rev. ST-AB 3,034202 (2000). 19. W. Paul and J. Baschnagel, Stochastic Processes: From Physics to Finance (Springer, Berlin, 2000) 20.

Thesis, University of Madras, 1997; R. Jagannathan and S. A. Khan, ICFA Beam Dynamics Newsletter 13, 21 (1997). R. Fedele and G. Miele, Nuovo Cim. D13, 1527 (1991); R. Fedele and V. I. Man’ko, in QABP-I; M. A. Man’ko, in QABP-IIand references therein; S. A. Khan and M. Pusterla, Eur. Phys. J. A7, 583 (2000); M. Pusterla, in QABP-11, this Proceedings and references therein. N. Cufaro Petroni, S. De Martino, S. De Siena, and F. Illuminati, in QABP-I, QABP-11, this Proceedings and references therein.

The last spin-dependent term accounts for the Stern-Gerlach kicks in the transverse phase-space and the Thomas-Bargmann-Michel-Telegdispin evolution. l2 The following interesting aspect of quantum beam optics should be mentioned. In the case of a spin-0 particle also one can derive the quantum beam optical Hamiltonian 'I? 8 It would also contain all the terms corresponding to the classical theory plus the quantum correction terms. But, these quantum correction terms are not identical to the quantum correction terms in the Dirac case.

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