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Unformatted text preview: eigenfunctions, (10.9) (The functions and are the normalised first and second states of the harmonic oscillator, with energies and .) Thus we now kow the wave function for all time: (10.10) In figure 10.1 we plot this quantity for a few times. Figure 10.1: The wave function ( 10.10 ) for a few values of the time . The solid line is the real part, and the dashed line the imaginary part. The best way to visualize what is happening is to look at the probability density, (10.11) This clearly oscillates with frequency . how that . Another way to look at that is to calculate the expectation value of : (10.12) This once again exhibits oscillatory behaviour!...
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 Fall '10
 DavidJudd
 Physics, mechanics, wave function, Eigenfunctions

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