606 Appendix: Problem Index
Location of singularities of
(4Z^3 − 2 Z+1)(Z−3)−^2 (Z−i)−^1 (Z+ 1 − 2 i)−^11.85
Residues of (Z−1)−^1 (Z+2)−^2 at polesZ=1 andZ=−21.86
Laurent series about singularity for e∫ x(Z−2)−^2 1.87
∞
0 (x(^4) +1)− (^1) dx 1.88
1.2.12 Calculus of Variation
Curve which has shortest length between two points 1.89
Brachistochrome (curve of quickest descent) 1.90
Equation to the surface of revolution of a soap film stretched
between two parallel circular wires.
1.91
Sphere is the solid of revolution which for a given surface area
has maximum volume1.92
1.2.13 Statistical Distributions
Poisson(px) (a) Normalization ofpx(b)<x>=m(c)σ=√
m
(d)pm− 1 =pm(e)px− 1 =(x/m)pm&px+ 1 =mpx/(x+1)1.93
Binomial (Bx) (a) Normalization ofBx(b)<x>=Np(c)
σ=√
Npq1.94
S.D. with net counts due to source, given total count rate and
background rate1.95
(a) Whenpis fixedB(x)→Normal asN→∞
(b) When Np is fixed B(x)→P(x) asN→∞ 1.96
Ifbis background counting rate andgbackground plus source,
for minimum statistical errortb/tg=√
b
g1.97
Radioactivity equation, decay constant and half-life from data on
activity measured after each hour1.98
Interval distribution and exponential law of radioactivity 1.99
Carbon dating experiment 1.100
Best fit for a parabolic curve 1.101
Relative precision of capacitance, given errors in the radii of
concentric cylinder1.102
Mean and most probable value of x for the probability
distributionf(x)=xexp(−x/λ)1.103
1.2.14 Numerical Integration∫
10
1 x(^2) dxby Trapezoidal rule 1.104
∫ 10
1 x
(^2) dxby Simpson’s rule 1.105
Chapter 2 Quantum Mechanics-1
2.2.1 de Broglie Waves
Photon energy and wavelength 2.1
Wavelength of electrons accelerated by P.D 2.2
Wavelength of neutron 2.3
For electronλ=(150/V)^1 /^2 2.4