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4 Jan 2023: H. (a). (b). Figure 1.2: Phase diagrams of (a) the liquid-gas transition, and (b) the ferromagnetictransition. ... zero. In a liquid, the natural path is one in which temperature is variedat constant pressure (b′ c′ d′ in Fig.

7 Jan 2023: a b = [(a b′) (b a′), a′ b′]=. [(b′ a) (a′ b), b′ a′]. ... Thus(a c′) (b b′) = ((a c′) b) b′ = (a (c′ b)) b′. =

11 Jan 2023: An electron is at rest in the presence of a magnetic field B = (B, 0, 0) andexperiences an interaction of µσ B. ... 1. s2d. ds. (s2dψ. ds. )=. {ψn, ψ > 0,. 0 , ψ 0, (). where s = r/b, b = (4πGΨn10 C)1. 2 and ψ = Ψ/Ψ0 with Ψ0 = Ψ(0).

11 Jan 2023: Derive shock jump conditions analogous to the three Rankine-Hugoniotrelations if,. a) B = (B, 0, 0),. ... b) B = (0,B, 0). Discuss the physical meaning of the jump condition related to the momen-tum equation in these two cases.

11 Jan 2023: Sketch the shift in the (U–B, B–V )two-colour plane, specifying the slope and indicating the direction of increasingextinction. ... Discuss under what circumstances the position of a star in the (U–B, B–V ) two-colour plane can be used to infer

11 Jan 2023: Show that. [b, b†] = 1. Consider the Hamiltonian. H = ǫa†a 1. ... 2. ǫ2 λ2. (. bb† b†b). ǫ2. ,. for some suitable choice of θ which should be determined.

11 Jan 2023: H0 =(a†a 1. 2. ) 2. (b†b 1. 2. ),. where [a,a†] = 1, [b,b†] = 1 and all other commutators are zero. ... 14θgab, or otherwise, that. dθ. dτ 1. 4θ2 R00 ,. where R00 = RabVaV b and.

11 Jan 2023: a) no magnetic fields are present;. (b) a uniform vertical magnetic field is present;. ... Find the probability that it makes a transition tothe state with opposite spin by assuming b B and using () from Part (i).

11 Jan 2023: An electron is at rest in the presence of a magnetic field B = (B, 0, 0) andexperiences an interaction of µσ B. ... 1. s2d. ds. (s2dψ. ds. )=. {ψn, ψ > 0,. 0 , ψ 0, (). where s = r/b, b = (4πGΨn10 C)1. 2 and ψ = Ψ/Ψ0 with Ψ0 = Ψ(0).

11 Jan 2023: Derive shock jump conditions analogous to the three Rankine-Hugoniotrelations if,. a) B = (B, 0, 0),. ... b) B = (0,B, 0). Discuss the physical meaning of the jump condition related to the momen-tum equation in these two cases.