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27 Nov 2009: K 2 = k2 U0. With kR ' 1, K % U1/20 (1 O(k2/U0)), find scattering length,. ... σtot %4π. k2sin2 δ0(k) % 4πR2. (tan(KR). KR 1. )2, K % U1/20.

8 Oct 2009: E = ma2V 20. 2!2. Indeed, the solution is unique. An attractive δ-function potential hosts onlyone bound state. '

22 Nov 2009: Synopsis: Lectures 20-24. 15 Scattering theory. Elastic scattering; cross section; method of particle waves; Bornapproximation; scattering of identical particles.

18 Nov 2009: 20 (mass m and asymptotic speed v0), incident upon a. target with a central potential V (r). ... k cot δ0 = 1a0. 12r0k. 2 ,. where a0 = (1 tan γγ )R, with γ = U1/20 R, defines the scattering length, and r0 is.

9 Nov 2009: 2mω2x 20 , i.e. x0 =. 2E. mω2. Over periodic cycle, the classical action is given by. ... 2. p(x)exp. ( E!ω. [xx0. x 2. x 20 1 arccosh.

27 Nov 2009: non-examinable in this course. Synopsis: Lectures 20-24. 15 Scattering theory†Elastic and inelastic scattering; †method of particle waves; †Bornseries expansion; Born approximation from Fermi’s Golden rule;†scattering of

9 Nov 2009: Degeneracy 2 2 6 2 6 2 10 6 2 10 Cumulative 2 4 10 12 18 20 30 36 38 48. ... Central field approximation: conclusions. Subshell name 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d Cumulative 2 4 10 12 18 20 30 36 38 48.

8 Oct 2009: 3.1. OPERATORS 20. 3.1 Operators. An operator  is a “mathematical object” that maps one state vector, |ψ〉,into another, |φ〉, i.e.

8 Oct 2009: a 20% admixture of the first excited state. Then the wavefunction isoff by ca. ... 20%, but the energy estimate will be too high by only 0.04(E1E0),usually a much smaller error!

28 Oct 2009: e.g. if optimum state includes ca. 20% admixtue of first excitedstate |αmin〉 = 110.22 (|0〉 0.2|1〉), energy estimate will be toohigh by only,.