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17 Jun 2019: If ka is the tangent vector to the trajectory of a photon and ua is the four-velocity ofa comoving observer (i.e., an observer at rest in the

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

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 = E0 α 2Acos ka. Using the fact that ψ0(x) is a parity eigenstate show that. (

17 Jun 2019: as. ka;b = 0. for a certain covector field ka, which you should define.

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

17 Jun 2019: µx ik[σ3,µ] Qµ = 0,. andµt 2ik2[σ3,µ] (kA B)µ = 0.

17 Jun 2019: ka = π α iγ. where, to leading order in 1/(U0a),.

17 Jun 2019: E(k) = E0 2J cos(ka). Define the Brillouin zone. Determine the number of states in the Brillouin zone.

17 Jun 2019: Deduce that, whateverparametrization ν is used along the curve γ, the tangent vector Ka to γ satisfies. (