Synoptic classification of living organism by R.S.K. Barnes

By R.S.K. Barnes

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Microreversibility proof for moving expansion functions I next shall prove (114). To do so in the present rather complicated situation, it appears most convenient to proceed indirectly, along lines analogous to (15)—(18). First I shall show that the analogue of (15 a) holds in the impact parameter coupled state approximation, with moving expansion functions, where Φ|(ί), ^f(0 are two functions obeying (76) and having expansions of the form (108b). , ^ f ( 0 is prescribed by the final condi­ tions that cf(t) in (115) equals cf(r) in (110a) when t = r.

116a) 40 E. Gerjuoy, Detailed balancing in the time-dependent impact parameter method Equation (116a) is 0 = cf^Aìci + c^À{c{ + c^Aìcì (116b) using (78) and (109b). But (116c) τ ^ Γ 1 ^ = i ^ r 1 f ί-^Γ 1 *! while bothi4j(0 and K{(f) are Hermitian, recalling (79c) and (89a). Thus (116b) reduces to (116d) ctUl^Ar1Xi-Ai-1B^ei. + Moreover, w-s4v-(M)f** (117a) ^•* -(£*/) f v */(£**)■ (117b) Equations (117a)—(117b), together with (79b), mean (117c) Employing (117c) in (116d) demonstrates that (116a) indeed is true.

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