Eigenfunctions o1

# Eigenfunctions o1 - corresponds to measuring Using(8.17 we...

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Eigenfunctions of The operator is . Solving the equation (8.14) we get (8.15) with solution (8.16) a ``plane wave''. As we have seen before these states aren't normalised either! Expectation value of and for the harmonic oscillator As an example of all we have discussed let us look at the harmonic oscillator. Suppose we measure the average deviation from equilibrium for a harmonic oscillator in its ground state. This

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Unformatted text preview: corresponds to measuring . Using (8.17 ) we find that (8.18 ) Qn Why is it 0? Sinilarly, using and (8.19 ) we find (8.20 ) More challenging are the expectation values of and . Let me look at the first one first: (8.21 ) Now for , (8.22 ) Thus, (8.23 ) This is actually a form of the uncertainity relation, and shows that (8.24 )...
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## This note was uploaded on 11/09/2011 for the course PHY PHY2053 taught by Professor Davidjudd during the Fall '10 term at Broward College.

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Eigenfunctions o1 - corresponds to measuring Using(8.17 we...

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