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

20 Jul 2021: 1. ktan. ka. 2= 1. ltanh. la. 2. where. k =. 2mE. 2> 0 and l =. 2m(U0 E). 2> 0. (ii) Suppose that initially U0 = 0 and the particle is in

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

17 Jun 2019: ka = i log(t. rr′. ). Part II, 2013 List of Questions [TURN OVER.

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

30 Aug 2019: b) When ka 1, approximate the dispersion relation by. D(k, ω) D approx(k, ω) 2ω 2ka 2k2a2.

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: E(k) = E0 2J cos(ka). Define the Brillouin zone. Determine the number of states in the Brillouin zone. ... ka = π α iγ ,. where α and γ are real and.

30 Aug 2019: MATHEMATICAL TRIPOS Part III. Wednesday, 8 June, 2011 9:00 am to 12:00 pm. PAPER 53. COSMOLOGY. Attempt no more than THREE questions. There are FOUR questions in total. The questions carry equal weight. STATIONERY REQUIREMENTS SPECIAL REQUIREMENTS.

17 Jun 2019: Let K denote the 2n2n matrix with n copies of J1 on the diagonal,and zeros elsewhere, and suppose that KA = AK.