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17 Jun 2019: Giventhat. 〈x〉 = 12k. (ka tan ka),. discuss briefly the possibility of 〈x〉 being greater than a. ... Hint: consider the graph ofka cot ka against ka.]. Part IB, 2010 List of Questions.

17 Jun 2019: For all N, find integers ka(N) and kb(N)such that. kb(N). k=ka(N).

17 Jun 2019: cosh kx cosh ka),. where k is a constant such thatlk = 2 sinh ka.

17 Jun 2019: E =12(E0 E1 4A cos ka). 12. (E0 E1)2 16A2 cos2 ka.

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.

17 Jun 2019: cosh kx cosh ka),. where k is a constant such thatlk = 2 sinh ka. ... Let K denote the 2n2n matrix with n copies of J1 on the diagonal,and zeros elsewhere, and suppose that KA = AK.

17 Jun 2019: tan(ka δ0). ka=. tan κa. κa,. where κ2 = k 2 γ 2. ... 42. Paper 2, Section II. 36B General Relativity. A vector field ka which satisfies.

17 Jun 2019: By considering the s-wave solution to the Schrödinger equation,. show thattan(ka δ0). ... ka=. tanh(. γ2 k2a). γ2 k2a. For low momenta, ka 1, compute the s-wave contribution to the total cross-section.Comment on the physical interpretation of your

17 Jun 2019: E =1. 2(E0 E1 4 A cos ka). 1. 2. (E0 E1)2 16 A2 cos2 ka.

17 Jun 2019: tanh (κa). κa=. tan (ka δ0). ka. where κ2 = γ2 k2.