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homework02

# homework02 - 4 Show that an electron and a positron(an...

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Phys 221 Homework II Due: Due Friday, February 3 1. Given the rule for multiplying 4-vectors (the notation below from the 1/27 lecture varies from Harris’s section 2.10 – but the results are equivalent): ˜ a · ˜ b =( a 0 ,±a ) · ( b 0 , ± b )= a 0 b 0 - ±a · ± b And that ˜ x ( ct, ±x ), show that ˜ x 2 is an invariant. Note : Do this by transforming ˜ x to another frame using the Lorentz Transformations. 2. Harris 2.76 3. Repeat Harris 2.76 parts (b) and (c), but instead of using the velocity transformation to switch frames use the Lorentz transformation: p ± = γ ( p - vE c 2 ) E ± = γ ( E - vp ) Find the momenta in the new frame directly and verify that momentum is conserved. (You won’t need the energy transformation – listed for completeness.)
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Unformatted text preview: 4. Show that an electron and a positron (an anti-electron, it has the same mass and op-posite charge), cannot annihilate into a single photon. Consider energy and momentum conservation to solve this. 5. Harris 2.84: provide your answers in MeV, note that m e = 0 . 511 MeV c 2 . 6. Harris 2.90: provide energy in MeV, mass in MeV c 2 , speed as a fraction of c. (u = 931 . 5 MeV c 2 ). 7. Harris 2.93 8. Harris 2.112: you may omit part c) Course Web Site: http://www.phys.cwru.edu/courses/p221/ \$Date: 2012/01/28 20:42:33 \$...
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