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ps2_1985 - MIT OpenCourseWare http/ocw.mit.edu 5.80...

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MIT OpenCourseWare http://ocw.mit.edu 5.80 Small-Molecule Spectroscopy and Dynamics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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MASSACHUSETTS INSTITUTE OF TECHNOLOGY± Chemistry 5.76 ± Spring 1985 ± Problem Set #2 1. The number of possible spin eigenfunctions for a single particle of spin I is 2 I + 1. (a) How many linearly independent spin eigenfunctions are possible for two equivalent particles of spin I ? (b) For a particle with I = 1, denote the three spin eigenfunctions by α , β , and γ , corresponding to the eigen- values M z = + , 0, . How many linearly independent symmetric and how many linearly independent antisymmetric spin states are there for two equivalent particles with I = 1?
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5.76 Problem Set #2 ANSWERS 1985 Page 2 2. Atomic eigenfunctions contain a factor exp( iM φ ). When the atom is a magnetic field B , the quantum number M represents the projection of the J –vector on B ( J M + J ). The usual selection rules for L , S , and J still hold for moderate B ,
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