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25 Jan 2007: es = cos φ i sin φ j, eφ = sin φ i cos φ j, ez = k. ... For (iii), from a decent diagram of spherical polars, find k = er cos θ eθ sin θ. ].

25 Jan 2007: with no dependence on and ) is = a br: (116)Next we have solutions, like the dipole potential, / cos , = Er cos cr2 cos : (117)What E does the rst term give? ... Hence, from (186)B = 0I4 Z 11 sdz0(s2 z02)3=2 e= 0I4s Z =2=2 cos d e; (z0 = stan)= 0I2se:

27 Nov 2007: asin2. nπx. a=. 1. a. (1 cos 2nπx. a. ). What is a probability that a particle described by ψn is between 0 and x0? ... Fn(x0) =. x00. 1. a. (1 cos 2nπx. a. )dx =. (x0a 1. 2nπsin. 2nπx0a. ). The classical distribution would be F(x0) = x0/a = limn Fn

25 Jan 2007: pair abmeans add or subtract the same expression with a and b interchanged. ... cos θ =gabU. aV b. |U a||V b|. (103). If the two vectors are timelike, and both are future directed, the rapidity θbetween them is given by.

6 Nov 2007: P is an orthogonal matrix and has the form. P =. (. cos φ sin φsin φ cos φ. ). , cot 2φ = e2K sinh B. ... λN+ λN. cos 2φ as N. This is the result we have already derived in (25).