Phys 402 Spring 2009 Homework 5 Due Friday, March 13, 2009 @ 9 AM 1. Griffiths, 2nd Edition, Problem 6.38 Hyperfine transition in the ground state of Deuterium. Find the hyperfine states by combining spin-1 with spin-1/2. 2. Griffiths, 2nd Edition, Problem 4.34 Raising and lowering operations on the coupled spin states |1 0>, |0 0>. S2 calculation. 3. Griffiths, 2nd Edition, Problem 5.4 Carry out the normalization of symmetrized wavefunctions 4. Griffiths, 2nd Edition, Problem 5.5 2-particles in the infinite square well. Ground state and first two excited state wavefunctions for distinguishable, fermion and boson particles. Extra Credit #7 Griffiths, 2nd Edition, Problem 6.21 Zeeman Effect in Hydrogen for n = 2 Extra Credit #8 Griffiths, 2nd Edition, Problem 4.56 (a) only Generating function for rotationsPhysics 402 Spring 2009 Prof. Anlage Discussion Worksheet for March 11, 2009 1. The Slater determinant is a very handy way to construct antisymmetric wavefunctions of N-identical particle systems. Suppose you want to distribute particles into states a, b, c, etc. One forms rows of a determinant made up of ψa(1) ψb(1) ψc(1) … followed by the next row, written as ψa(2) ψb(2) ψc(2) … , where “1” and “2” represent the coordinates of particle 1, particle 2, etc. Multiply the determinant by !/1 N for normalization. a) Form the antisymmetric wavefunction for two identical particles in states a and b. b) Form the antisymmetric wavefunction for three identical particles in states a, b and c. See what happens if a and c are the same state.2. Consider a spin-1/2 particle. It is known to be in the “up” state after a measurement of . Show that in this state zS 0==yxSS . Explain this result
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