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25 Jan 2010: x/a = θ sin φ (θ φ) cos φ ,y/a = 1 cos φ (θ φ) sin φ. ... A. (TURN OVER for continuation of question 4. 4. (d) By considering a wave solution of the form ϕ = C cos(kxωt) for auniform rod, find the dispersion relation and the

4 Apr 2010: r(t) = A cos(ωt) B sin(ωt). Applying the boundary conditions r(0) = 0 and r(t̄) = r̄ we find A = 0 andB = r̄/ sin(ωt̄),. ... cos qd D q2. 2+. Inverting and applying the inverse Fourier transform, we obtain.

30 Dec 2010: By. are shown in Fig. 3. They are related by kAy kBy = 2π α.1Hence, cos(kA(B)y ) = cos(kB(A)y 2π α), so the Hamiltonian (8)is the ... GW〉 =j. [cos θj sin θj eiφj â†j ]|0〉. (20). In the hard-core limit [as expressed by Eq.