PHY 504
Problem Set #1
due 3 September 2010
1. A circular platform rotates in the horizontal plane about its center with frequency . In this problem, you may ignore motion in the vertical direction an
(f) Cross product is not associative (see (d), has no identity and no inverse.
2.
Since (Mi)jk = -ijk ,
[ M i , M j ] mn = ( M i ) mk ( M j ) kn ( M j ) mk ( M i ) kn
= imk jkn jmk ikn = imk jnk + jmk
PHY 504
Problem Set #11
due 22 November 2010 1. Consider a system of N coupled oscillators like those in Figure 13.1, except that these oscillate transversely in the vertical direction only. Assume th
PHY 504
Problem Set #3
due 17 September 2010 1. Derivation 2.8. 2. A particle of mass m moves in a potential sin .
(a) Write down a Lagrangian and obtain Lagranges equation from it. (b) Solve the equa
PHY 504
Problem Set #4
due 24 September 2010
1. Goldstein Exercise 2.12. Show that the Lagrangian at the end of the problem differs from a more familiar Lagrangian by a term which is a total time deri
PHY 504
Problem Set #5
due 1 October 2010
1. A particle of mass m moves in a uniform magnetic field of magnitude B. (a) Write down a Lagrangian describing this system and the resulting equations of mo
PHY 504
Problem Set #6
due 15 October 2010 1. For the attractive inverse-square potential
(a) Calculate the differential cross section (). (b) Calculate the capture cross section. This is defined to b
PHY 504
Problem Set #7
due 22 October 2010
1. Derivation 4.14. Use these formulas to obtain expressions involving dot products for (a b) c, a (b c), and (a b) (c d). Give three reasons why vectors do
PHY 504
Problem Set #8
due 29 October 2010 1. Problem 4.15. 2. A rotation about the z-axis by is followed by a rotation about the x ' axis by . What is the axis and angle of the resulting rotation?
3
PHY 504
Problem Set #9
due 5 November 2010 1. Show that ijk is invariant under rotations, assuming that it transforms as a 3index tensor:
i + j + k + = Ai + i A j + j Ak + k ijk
2. A solid rectangul
PHY 504
Problem Set #10
due 10 November 2009 1. The Lennard-Jones potential models the interaction between a pair of neutral atoms:
V ( r) =
AB r12 r 6
where the first term represents a van der Waals
PHY 504
Problem Set #2
due 10 September 2010
1. A diatomic molecule consists of two atoms with unequal masses, bound by a linear force derived from the potential | | , where a is the equilibrium inter