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Unformatted text preview: principle. 6. (20 points) Consider the Hamiltonian H = p 2 1 2 m 1 + p 2 2 2 m 2 + V ( x 1x 2 ) . (a) Show that in general [ H, p 1 ] and [ H, p 2 ] are nonzero. (b) Show that in terms of P = p 1 + p 2 , X = m 1 x 1 + m 2 x 2 m 1 + m 2 (1) p = m 2 p 1m 1 p 2 m 1 + m 2 , x = x 1x 2 (2) [ P, X ] = [ p, x ] =i h are the only nonvanishing commutators among this set. (c) Find H ( P, p, X, x ). (d) What is a complete set of commuting operators for this system? Assume that V has only bound states (no continuum states)....
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This document was uploaded on 09/10/2009.
 Spring '09
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