Eigenfunctions of

Eigenfunctions of - Actually, once we know the ground...

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Eigenfunctions of through ladder operations If we start with the ground state we would expect that we can't go any lower, (9.17) This can of course be checked explicitly, 0 (9.18) Can you show that using the operators ? Once we know that , repeated application of Eq. ( 9.15 ) shows that , which we know to be correct from our previous treatment.
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Unformatted text preview: Actually, once we know the ground state, we can now easily determine all the Hermite polynomials up to a normalisation constant: (9.19) Indeed . From math books we can learn that the standard definition of the Hermite polynomials corresponds to (9.20) We thus learn and . rove this last relation....
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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 of - Actually, once we know the ground...

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