Now where does the probability peak

Now where does the probability peak - Figure 11.2: The...

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Now where does the probability peak? Clearly the probability density to find an electron at point is (11.22) but what is the probability to find the electron at a distance from the proton? The key point to realise is that for each value of the electron can be anywhere on the surface of a sphere of radius , so that for larger more points contribute than for smaller . This is exactly the source of the factor in the normalisation integral. The probability to find a certain value of is thus (11.23)
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Unformatted text preview: Figure 11.2: The probability to find a certain value of for the first two Harmonic oscillator wave functions. These probabilities are sketched in Fig. 11.2 . The peaks are of some interest, since they show where the electrons are most likely to be found. Let's investigate this mathematically: (11.24) if we differentiate with respect to , we get (11.25) This is zero at . For the first excited state this gets a little more complicated, and we will have to work harder to find the answer....
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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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