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Unformatted text preview: oscillator: v | x | v = v x v dx = unless v = v 1 and v + 1 | x | v = (2 ) 1 / 2 ( v + 1) 1 / 2 v 1 | x | v = (2 ) 1 / 2 ( v ) 1 / 2 where = 4 2 m / h , and = 2 1 [ k / ] 1 / 2 is the vibrational harmonic frequency. Evaluate the nonzero matrix elements of x 2 , x 3 , and x 4 ; that is, evaluate the integrals v | x r | v = v x r v dx for r = 2 , 3, and 4 (without actually doing the explicit integrals, of course!). (b) From the results of part a, evaluate the average values of x , x 2 , x 3 , and x 4 in the v th vibrational state. Is it true that x 2 = ( x ) 2 , or that x 4 = ( x 2 ) 2 ? What conclusions can you draw about the results of a measurement of x in the v th vibrational state?...
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- Spring '04