1. Physics Work-out #2
April 30, 2011
Jackson’s Classical Electrodynamics 1.12:
Prove Green’s reciprocation theorem: If Φ is the potential due to a volume-
charge density ρ within a volume V and a surface-charge desntiy σ on the con-
ducting surface S (∂V ) bounding the surface V , while Φ is the potential due to
another charge distribution ρ and σ , then
ρΦ 3
+ σΦ = ρΦ 3
+ σΦ
V ∂V V ∂V
Sakurai’s Modern Quantum Mechanics 2.29:
Define the partition function as
Z= 3
K( ; 0)|β= /
Show that the ground-state energy is obtained by taking
1 ∂Z
− (β → ∞)
Z ∂β
Illustrate this for a particle in a one-dimensional box.
Goldstein’s Classical Mechanics 2.4:
Show that the geodesics of a spherical surface are great circles, i.e., circles
whose centers lie at the center of the sphere.
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