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7 Jan 2019: 2mṙθ̇ mrθ̈ = ka sin(θ θB). d. dt. L. ṙ=L. ... r= mr̈ = mrθ̇2 kr ka cos(θ θB). d. dt. L.

6 Nov 2019: or B = 0 , cos(ka) = 0 ,. ψ(x) = A cos(kx) , k =nπ. ... C cos(la) = A exp(ka) , (4.40)lC sin(la) = kA exp(ka).

23 Nov 2019: 113] and Joubouri et al.[118] – the latter has been corrected to the Co Ka wavelengthto permit the comparison.

30 Apr 2019: For correspondence:. fmj1001@cam.ac.uk (FMJ);. b.longdon2@exeter.ac.uk (BL). †These authors contributed. equally to this work. Competing interests: The. authors declare that no. competing interests exist. Funding: See page 16. Received: 03 March

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.

19 Jul 2019: value. E = E0 2t cos(ka) (2.5). The spectrum is shown in the figure for t > 0.

19 Jul 2019: structure. E = C cos(ka). Then the velocity in a constant electric field oscillates as. ... v(k) =Ca. sin(ka) = Ca. sineEa t. The Bloch frequency is! =

19 Jul 2019: q. kA(eiqa/2 eiqa/2). Notice that only the combination (r t) appears.

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.

22 Aug 2019: c0= ka 1 ,. a ‘small’ sphere to be one such that a 2πc0ω. , ... i.e.ωa. c0= ka 1 ,. Mathematical Tripos: Part II Waves 16 S.J.Cowley@maths.cam.ac.uk, Lent 2019.