An Introduction To Mechanics

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Unformatted text preview: Lucky Problem Set 13 Physics 116 : Due Slope Day The final exam will be held in Rockefeller 115 on Tuesday, May 13 at 2:00-4:30 PM. 1. Show that the relativistic forms for momentum and energy reduce to the Newtonian form at slow speeds of both the particle and the moving frame, S (i.e both v c and u c). Hint : Use a Taylor series expansion and don't worry about any constant offset terms. 2. K&K, Problem 13.2 3. K&K, Problem 13.5 4. K&K, Problem 13.10 5. The 0 meson has a rest mass of m c2 = 135 MeV and decays into two photons a) Find the energy of the two photons if the 0 meson is at rest when it decays. b) Now assume that the 0 meson has an energy of 1 GeV relative to the lab frame at the time it decays. Find the energies of the two photons in the lab, if one of the photons emerges directly parallel to the direction that the 0 was originally traveling. 6. In the mean field approximation, a fermionic system with S = 1/2 and an effective attractive interaction (U < 0) becomes unstable at low temperatures. The critical temperature Tc is defined by the condition = 1 - U where is the susceptibility. Calculate Tc in the weak coupling limit, U EF where EF is the Fermi energy and N (EF ) is the density of states at the Fermi energy. Seriously though, have a great Slope Day! ...
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