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13 Mar 2019: δ(r a). Show that the phase shifts are given by. tan δl = kλa2[jl(ka)]. ... 2. 1 kλa2jl(ka)nl(ka). [Hint: The δ-function leads to two continuity conditions at r = a.

22 Aug 2019: Archaeology at Cambridge. 2009–2010. McDonald Institute for Archaeological Research. ContactsMcDonald Institute for Archaeological ResearchDowning Street, Cambridge, CB2 3ER, UKwww.mcdonald.cam.ac.ukReception 44 (0)1223 333538Graeme Barker

22 Aug 2019: Archaeology at Cambridge. 2009–2010. McDonald Institute for Archaeological Research. ContactsMcDonald Institute for Archaeological ResearchDowning Street, Cambridge, CB2 3ER, UKwww.mcdonald.cam.ac.ukReception 44 (0)1223 333538Graeme Barker

7 Nov 2019: C A M B R I D G E U N I V E R S I T Y. REPORTERS p e c i a l N o 2 W e d n e s d ay 6 N o v e m b e r 2 0 1 9 Vol c l. P U B L I S H E D B Y A U T H O R I T Y. R O L L O F T H E R E G E N T H O U S E A N D L I S T O F M E M B E R S O F T H E FA C U

30 Aug 2019: 2. 1 (i) If A > 0 and N is a positive integer, define KA,N : T2 R by. ... and1. (2π)2. T2. KA,N (s, t) ds dt = 1. By considering functions of the form.

19 Jul 2019: 2=. mM. hm M. p(m M)2 4mM cos2(ka). i. The resulting dispersion relation is sketched in Figure 57 in the first Brillouin zone. ... This is because it is. valid only at long wavelengths, ka 1.

17 Jun 2019: Let. Q(k) = aR′ (a)R(a). kaj′ (ka)j(ka). Obtain the relation. tan δ =Q(k)j2(ka)ka. ... Q(k)n(ka)j(ka)ka 1. Suppose thattan δ. γ. k0 k,. for some , with all other δ small for k k0.

30 Aug 2019: Show that a Killing covector ka satisfies. ka;bc = Rabcdkd. A spacetime is said to be static if it possesses a timelike Killing covector ka whichis hypersurface-orthogonal. ... with ρ p > 0 then the fluid 4-velocity ua is parallel to ka. [

18 Oct 2019: non-negative, because. n = nhn|ni = hn|N |ni = hn|A†A|ni = kA|nik2 0 (3.11). ... Taking the norm of both sides shows that. |cn|2 = kA†|nik2 = hn|AA†|ni = hn|N 1|ni = n 1.

17 Jun 2019: Let. KA = {X Mnn(R) | [A, X] = 0}LA = {[A, X] | X Mnn(R)}. ... Show that KA and LA are linear subspaces of Mnn(R). If A and B are similar, showthat KA = KB and LA = LB.