606
Appendix: Problem Index
Location of singularities of
(4Z
3
− 2Z + 1)(Z − 3)
−2 (Z − i)
−1 (Z + 1 − 2i)
−1
1.85
Residues of (Z − 1)
−1 (Z + 2)
−2 at poles Z = 1 and Z = −2
1.86
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 volume
1.92
1.2.13 Statistical Distributions
Poisson( p x ) (a) Normalization of p x (b) = m (c) σ =
√
m
(d) p m−1 = p m (e) p x−1 = (x/m) p m & p x+1 = mp x /(x + 1)
1.93
Binomial (B x ) (a) Normalization of B x (b) = Np (c)
σ =
√
Npq
1.94
S.D. with net counts due to source, given total count rate and
background rate
1.95
(a) When p is fixed B(x) → Normal as N → ∞
(b) When Np is fixed B(x) → P(x) as N → ∞
1.96
If b is background counting rate and g background plus source,
for minimum statistical error t b /t g =
b
g
1.97
Radioactivity equation, decay constant and half-life from data on
activity measured after each hour
1.98
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 cylinder
1.102
Mean and most probable value of x for the probability
distribution f (x) = x exp(−x/λ)
1.103
1.2.14 Numerical Integration
10
1 x
2 dx by Trapezoidal rule
1.104
10
1 x
2 dx by 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 electron λ = (150/V )
1/2
2.4