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Quantum Mechanics in Mathematics, Chemistry, and Physics by Volker Enss, Barry Simon (auth.), Karl E. Gustafson, William

By Volker Enss, Barry Simon (auth.), Karl E. Gustafson, William P. Reinhardt (eds.)

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6) ¢a is a function of one variable, the relative coordinate of the two centers of mass. ) The total cross section is now defined analogously. In addition to the clusters which are scattered elastically and deflected one also counts all excitations, breakup and rearrangement collisions. 7) v. ENSS AND 24 B. SIMON where n. are the corresponding bound state wave functions (or one ~ if the cluster consists of a single particle) and g is the familiar plane wave packet for the relative center of mass motion, obtained as a limit of square integrable functions as discussed in Section 3.

8[1\1> OJ satisfy all the 24) properties except possibly i) 57 REAL AXIS ASYMPTOTICS (satisfaction of 17) on (O,y)uf:/,+, if (O)y)v(y)t«J)h then 17) holds over and only if over all z € D+ having 0 < R[z] 1= Y holds The I[A] < 0 case with J-, E_, D_ q To see 25), first notice the (so z = X € (0,+00» I[z] goes similarly. = 0 special case of 26) is clearly equivalent to 17) by contour deformation in 19), taking into account the 21) and 24) jumps on the verticals R[s] = R[z] and R[s] = y. Thus the general 26) implies 17), and the converse implication follows by unique analytic continuation of boundary values, after first rewriting (by means of 21» the sum of the 26) right side first two terms in an equivalent form assuring analyticity in z.

5. 6. 7. 8. 9. E. J. HELLER ET AL. G. Herzberg, Molecular Structure and Molecular Spectra II. Infrared and Raman Spectra of Polyatomic Molecules. (Van Nostrand, New York, 1945); III. Electronic Spectra and Electronic Structure of Polyatomic Molecules. (Van Nostrand, New York, 1966). R. G. Gordon, "Correlation Function for Molecular Motion", Adv. Mag. Res. 3:1 (1968). D. W. Oxtoby, Adv. Chem. Phys. 40:1 (1979). g. A. Messiah, Quantum Mechanics Vol. I (Wiley, New York, 1958) p. 216. g. J. E. Moyal, Proc.

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