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3 Jul 2024: Part II, Paper 4 [TURN OVER]. 24. 33B Principles of Quantum Mechanics(a) For a harmonic oscillator A of unit mass and frequency ω, write down the. ... Considersmall, sinusoidal perturbations to the edge of the gyre r = a η(θ,t), where η =ϵexp(ikθ

17 Jun 2019: as. ka;b = 0. for a certain covector field ka, which you should define. ... r ]. Part II, Paper 3 [TURN OVER. 24. 37B Waves.

17 Jun 2019: tan(ka δ0). ka=. tan κa. κa,. where κ2 = k 2 γ 2. ... Part II, 2010 List of Questions [TURN OVER. 24. Paper 1, Section II.

17 Jun 2019: Sketch the ground state energy eigenfunction χ(x) and show that its energy isE =. 2k2. 2m , where k satisfies. tan ka = k2mV0. 2 k2. ... 24. 2/I/5B Numerical Analysis. Applying the Gram–Schmidt orthogonalization, compute a “skinny”QR-factorization

4 Jul 2024: Part II, 2024 List of Questions [TURN OVER]. 24. Paper 4, Section I.

20 Jul 2021: 24. Paper 3, Section II. 9E Linear Algebra(a)(i) State the rank-nullity theorem. ... 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: By considering the s-wave solution to the Schrödinger equation,. show thattan(ka δ0). ... Part II, 2018 List of Questions [TURN OVER. 24. Paper 4, Section I.

17 Jun 2019: 24, 49,‘Total’ is the vector of Total in each category, taking values 117, 56,. , ... E =12(E0 E1 4A cos ka). 12. (E0 E1)2 16A2 cos2 ka.

17 Jun 2019: 24. Paper 2, Section II. 9F ProbabilityFor a positive integer N, p [0,1], and k {0,1,. ... For all N, find integers ka(N) and kb(N)such that. kb(N). k=ka(N).

17 Jun 2019: ka = i log(t. rr′. ). Part II, 2013 List of Questions [TURN OVER. ... 24. Paper 3, Section I. 10D CosmologyThe number densities of protons of mass mp or neutrons of mass mn in kinetic.